I disagree both, neither blitz doesnt represent chess strength nor blitz is indicator of chess strength is true. But both of them true partially.
Blitz strength is related to chess strength (a little bit imprecise because other factors also affects) but this statement holds only after some level, an 1300 OTB player may have 1500 blitz other 1500 OTB may have 1100 blitz (i have seen many examples) But lets say players stronger than 1600 OTB have blitz rating in range of their OTB rating +-200 Elo. Of course this also doesnt hold at the other side of continum. Lots of IM and GMS have 2700-3000 blitz rating with 2300-2500 OTB. We can assume after 2100-2200 level blitz tends to be +100/+700 range instead of -200/+200 range. Of course exceptions are always possible.
You're mistaken, at least for the ratings here on chess.com, which I'm referring to.
Play a 1200 here in 5-min blitz and compare in strength to a 1200 long-rated player here. The 5-min blitz player will be substantially stronger. And it's not because they're just so much better at blitz. They're just significantly better players.
For here, the starting level for any new player is 1200. That 1200 rating is given to new slow-time control players, but also to new blitz players.
Since most new players are nowhere near good enough to even survive a 5-min blitz game, they'll play mostly slow time control games. So you're dealing with a much more competitive pool of players in the blitz section here, since all the real newbs aren't even participating.
For the GM/master ranges, yes, it's more skill-specific related, I'll grant you that, but that is pretty irrelevant to our class-level ratings, and specific to chess.com which is what I'm referring to.
Even overall though, blitz ratings def do reflect one's skill to a large extent.
You finally make a little bit of sense here. What you're saying about the average 1200 in blitz being stronger than the average 1200 in standard is 100% true. Obviously. That isn't the same way the whole way up the ladder though. Once we get to 1400+, we're not really dealing with any beginners at all anymore. I think a 1600 classical is stronger than a 1600 blitz. It depends on the time control, of course, but in classical chess? Yeah...obviously the guy who specializes in classical OTB games should win. You know from everything you've read this week that there's no denying how beginners, improving club players, and even 1800'ish players are advised against playing much blitz. But forget 1800'ish - players in the 1200-1600 range are of course going to get more progress and improvement out of classical games than blitz games. You have to agree with that, no?
What is a little suspect though is your claim that you have a standard rating on BOTH Lichess and ICC of 1800+. Really? On ICC your standard is 1800+? There's really no reason to exaggerate or lie. As for Lichess: You know that Lichess ratings start at 1500 instead of 1200 like everywhere else and you also know that ICC is a much, much more competitive player pool than Lichess. That's why I find it odd that your rating would be the same in both ICC and Lichess. They're different rating systems and the strength of ICC's player pool is #1 on the internet. Lichess might even be the softest.
The debate isn't a blitz game vs a 15-minute game. The debate is 3 blitz games vs. one 15-minute game.
I'd say you gotta do a little of both.
I'm wondering if this is the case. Obviously, at any level where we're hanging pieces - It's too fast. Perhaps though mixing in a little of both is the answer. The thing is that if you were preparing for a tournament in a week - how would you spend that time? I guess you're saying a little bit of both and this would go in line with some stuff I've seen (like it matters) Magnus say on the subject. He has recommended playing as much as you can at all different time controls...which, especially considering the age he came up in, I'm sure is what he did. That's Magnus, though.