Chess.com Ratings are a JOKE

Sigh.  Good luck bud.  Lord knows, you are going to need it.

The only thing I'm speculating about is his actual playing strength.  I agree with your first point, and largely with your second (his OTB blitz rating is in line with his OTB classical rating, but I agree he has far less games OTB than he does online).  Would you expect someone who struggles OTB (in both classical and blitz) to be 2300+ online?  I expect his online ratings to be higher than his OTB ratings, but like I said, that is a large gap and would be highly unusual.  That said, it is possible for someone to do that by simply playing a ton of games with a slightly above average score (i.e. 52% win rate) for an extended period of time.  But that would not be a reflection of his actual playing strength, just that he played a ton of games.

If I didn't know his playstyle and if I assumed that the irl rating is the more accurate one I would also say that its unusual. Because I know it, it doesn't surprise me much. 
I mean.. right now I have played with a 2100 who didn't see a mate on one:
https://www.chess.com/analysis/game/live/50221162357 
and it was rapid.. in blitz are those mistakes even more often..  you don't need any deep strategy skills (what you need to be GM for example..) to you could be good in blitz I think.. you only need to see things fast

Well let's consider a little thought experiment:

(a) Suppose on-line chess ratings for all players are reset every year on the 1st of January, no exceptions.

(b) Suppose each year the initial rating varied, i.e. 1000 one year, 1500 the next etc.

Would there be any annual consistency in the average 31st of December ratings?

I am certain there would be no consistency whatsoever. I would even guess that there would be no dependency on the value of the January rating either.

The reason for the former conclusion is that the ELO system is a relative scale, i.e. there is no agent driving the average to a fixed value.  For example, consider IQ Tests, the average performance is always assigned 100, and the score is relative to this datum. This is not how an ELO system works, there is no inherent fixed point all is relative.

Jumping back to the real world, clearly with any on-line chess ELO system there is a 'shadow' fixed point, but this is not an average but an extreme, being the assigned ratings of most title players, which in turn are anchored by the histrionic performances of humans. Hence why there is a distinct rating conversion at the extreme levels of performance, irrespective of formats or platforms.

Clearly the farther you move away from the extreme the more inaccurate the ELO system will be. Thereby assigning yourself a much higher rating than merited by the average talent pool could be capable of gaining a rating advantage, as the average rating of the pool can't possibly be accurate.  Of course, consequences could be reversed if you assigned yourself the opposite. Why take the risk?

CCC should fix the starting rating as per LiChess at the average rating, this would remove some of the flakiness from the ratings.  You can argue the degree of difference which would result. But subjectively having played on both LiChess and CCC the former feels more solid, there are far fewer 'surprise' performances from the players once you get pass the '?' ratings.

At the very least fixing the starting rating to the pool average would protect beginners from a lot of toxic behaviours, i.e. fewer cheats, new-account-sandbaggers, bots and annoying speed-runs.

As to the inflated puzzle relative to gameplay ratings the reason for this characteristic is fairly simple. Consider two players with puzzle ratings of 2500, Player A spends no more than 10 seconds on any puzzle (typical GM level), whereas Player B is prepared to spend up to an hour on any given puzzle. Clearly you would expect Player B to have an inflated puzzle rating relative to their gameplay rating, and Player A to be more consistent.

The same applies to correspondence/daily ratings where the situation is much worst, as one player could be playing on one game a day and another 500+. BTW, this is not an extreme as about a quarter of CCC players play mainly correspondence/daily format and many have huge number of individual game moves per day. 

It's really doubtful whether using an ELO type rating system makes any sense at all for puzzles and the on-line correspondence/daily game format.

First of all, let's talk about what happens when a player is incorrectly rated. If they are not rated high enough, then they will achieve their correct rating by taking away points from other players. Those players will then be underrated, and take away from others, and so on, until in the limit we see the cost is evenly shared by the whole population. This doesn't matter when 1 player is underrated, but if, for example, 10,000 players are underrated by 100 points each, then a 1 million point cost will be evenly distributed to the whole population, so if there are 1 million players, everyone loses 1 rating point.

Elo and Glicko have safeguards against this by making it so new players gain (and lose) rating points more rapidly than their established opponents. Glicko does an even better job because not only is there an initial period of rapid rating change, but also inactive players have a more rapid rating change, and it's proportional to their inactivity.

All this to say that the starting rating on chess.com has a very small effect because the math of the rating system works to preserve the point-to-skill ratio.

It helps match players to puzzles that are challenging for them.

Because a 1600 rated bot doesnt play like a 1600 it plays like a super gm pretending to be 1600. It makes obvious blunders almost everyone can find while 1600s may make slight positional mistakes a higher rated player may capitalise on. In simple terms bots make good moves and suddenly decide to hang their queen. Real players play sub optimal moves almost every move with no significant way to capitalise on making it much harder to beat a 1600 rated player than an engine and sometimes players may play traps that arent the best move just so they can trick their opponents and even though at the high level that move may be terrible at the low level its a great move.

When you play ranked games against AI in a chess program there is no social connection, whether you are ranked 1600 or 2200 it has no social impact and I don't see the point of participating in the "ego cult" unless you are a narcissistic personality with an ego problem.    

The goal of the elo rating is the same as AI normal, AI hard, AI very hard etc. is to play a game where the difficulty level is not too high or too low for you, otherwise it's no fun.

On the internet there is not so much social connection and it should be the same except that it is not AI controlled opponents but humans. Whether you are 1600 or 2200 elo we don't care, the important thing is not to be well or badly classified but to fall on a level of difficulty which are not too weak or too strong, otherwise it's no fun.

So you'd prefer to start Kowarenai at 1500, heh.

Anyway, the point of starting everyone at the average rating is, in theory, the number and extent of overrated people is perfectly balanced by underrated, and therefore any effects cancel out.

I can't tell a difference. I think chess is the same on both sites (chess.com and lichess).

The biggest difference that comes to mind is how premoves work and if I time out when I have pawnless king + knight it's a draw on lichess but a loss on chess.com.

Umm... I think that's right? It's been a while since I've timed out like that, but that's my memory anyway.

I agree their policy on speed running is trash.

But on balance, there are over 1 million games played on chess.com every day... so letting some GM speedrun on Twitch does more good for chess.com than harm... from a business standpoint I mean.

I have never meet a speedrunner as far as I know. And I love to watch speedrunners on youtube because I learn a lot from it. I take this trade any day, the risk of facing them versus the awesome free content they give me.

I do not know if they still do this, but when Hikaru, Eric, and Naroditsky we're doing them regularly, once the run was finished all their opponents had their rating points refunded.

I know. I think they should tell the player they're playing a GM before the game begins.

Sure, I think it's fine to have GMs play low rated players... but don't display a fake rating to the low rated player.

Maybe it is because they want the opponent to act as if it is a normal game. They could have a pop up message after the game saying ”you have just played a GM and your rating will soon be refunded”

Personally, I would not be opposed to them banning speed runs.  It does not make sense to classify sandbagging as a fair play violation, but allow strong players to notify staff that they are going to create a new account specifically for the purpose of blowing through lower rated players for a few hundred games.  While the videos they produce are instructional, I don't see how they can justify maintaining the position of "sandbagging is cheating ... unless you tell us you are doing it first".  However, I also do not see it as a major problem nor one that is really holding anyone back.

The lower rated player is just trying to play chess, not be a less for someone.

If a 1200 wants to play a 3200 then the GM can play followers or something like this. There's no need for the website to help GMs trick people. I don't think it results in more instructive games to trick them.

Sure, I agree it's not a major problem.