How rare is it for a chess.com user to have balanced stats?

Generally, when I click on a player's profile, I would view their rapid, blitz, and bullet rating. However, it is uncommon for me to stumble upon a player with consistent rating in all three categories. Meaning the difference in ELO between three different time control is less than 50 (or sometimes even 100). What would be the reason or reasons for this? Does anyone have the same experience? Is it statistically unlikely? 

Thanks.

Basically the typical order of ratings goes rapid down to blitz down to bullet and it just comes down to the simple factor of time, people can usually play better moves if they have more time and to play at the same strength at a fast pace is often quiet challanging, i for example am an exception where i prefer faster play having my ratings be flipped of the typical with bullet down to blitz down to rapid

In Elo and Elo-like systems, rating distributions aren't enforced, but instead emerge based upon the matches played by the population. Even if the distributions were the same, it would be unlikely that a player had the same ability relative to the rest of the player base, regardless of time control.

I think it's a safe assumption that many players play the shorter time controls without learning how to play Chess well first. This is roughly analogous to speed-reading books without learning to read first. We should expect to see a skew towards the lower end of the rating distributions on shorter time controls.

I could do it if I wanted... but I don't wanna

This is a common mistake. Your opponent always has as much time as you do, so "having more time" is not the answer.

Ratings don't measure performance in an absolute sense (like measuring height or weight), they measure it in a relative sense (comparing you to others in that time control), so whether the sub-population (e.g. chess.com blitz) is more or less skilled as compared to chess players overall doesn't make a difference since a rating only compares an individual to others in that sub-population.

But maybe you didn't mean it like that. Sure, certain time controls attract beginners and repel experienced players. These time controls are known as "rapid"

It doesn't need a reason since different ratings are measuring different things.

The example I like is currency. 1 USD = 135 Japanese Yen. They are different numbers but equal in value. In this analogy your chess skill is something like gold, and different ratings on different sites are economies that represent that value with different numbers.

To know whether you're bad a blitz as compared to rapid, you'd need to know the average ratings of players who play the same time controls of blitz and rapid as you do... since no one collects this data, you generally have to do it yourself, after games, by looking at your opponent's profiles.

For players under 2000, rapid is likely to be your highest rating.
For players at the top, rapid is likely to be your lowest rating.

And it depends on the time control too. I was trying out some 2|1 which is classified as bullet... it was rare to find a player rated over 2000 in that time control. Meanwhile if I play 1|0 I'll be paired with someone close to my rating every time.

Just a fluke could be one.

A desire to see if it could be done.

A desire to be equally good across all time platforms rather than an emphasis on a high  rating in one, thereby playing more games at different times to keep them equal.

The shorter the time control, the stronger the pool and thus the lower the rating.

Most people have a favorite time control, or a general area, they tend not to play the unfavoured time controls. As a result a disparity in ranking.    

As long as the population represents a continuum of skill, having very strong players (like GMs) in the population doesn't affect anyone's rating. A 1500 will be a 1500 regardless of who is at the top.

The only time having extremely strong players would matter in that way is during the initial setup... for example if your first many players were GMs... but even then, because of the 100 rating floor, it would eventually become what it is today.

Some people play better under lower time constraints than others, so with more time the latter can play better overall, in some cases.

Not for weaker players.

But for stronger players, sure, partly because the glass ceiling of rapid is something like 2400, and partly because once you get that high you don't have anyone to play with.

For example I picked a random 2400 user from the leaderboard: @ichiban-misaka-simp
The highest rated rapid player they've beaten was rated 1800 and that was 4 years ago. Their actual highest rating was 1889. It's only 2400 because of the rating boost(s) chess.com has done in the past, and they're only on the leaderboard because of some unrated games they've played.

Sure, but also, some play better with tighter time constraints because they play BS, but they play it fast enough that their opponent burns more time than they do

@12
"why is shorter time control = stronger pool?"
++ Grandmasters play bullet, beginners slow time controls.
@14
"having very strong players (like GMs) in the population doesn't affect anyone's rating."
++ The GM gain rating at the expense of the rest.

Between established players, yes, when a player gains rating, the cost (so to speak) is paid for by everyone else, however Glicko creates and destroys points based on RD.

In the worst case scenario, let's say 1 million players signed up in order of strength, the first day starting with the best players. In that case, for a long time, many players would be pushed down to the floor, but points are created there too i.e. if I'm 100 and I lose to you, you gain points but I don't lose any... so eventually (after very many games) even in the worst case the rating distribution would end up being what it is today.

Funnily enough, the same wouldn't be true if they joined in order from worst to best. In that case ratings would be extremely high, and chess.com would probably want to decrease everyone's rating a few times before things settled.

Different people are playing different stuff. First of all, titled players play blitz and bullet mostly because they mostly play longer games over the board. Some are playing 10|0 rapid, but a lot less. The result is that up to 2 200 rapid rating, people will have a lower blitz rating in most cases (maybe not all, because some people are better in faster time controls). But because of this, there are a lot less people with 2 500+ rapid than there are such people with blitz rating.

So different pools + different preferences = different ratings across the board in most cases.

@19
At any moment more beginners join that grandmasters.
A beginner joins, gets an initial rating of 1200, plays rapid, loses, and descends to 900.
Then he has donated rating to the rapid pool.
A grandmaster joins, gets his initial rating, plays bullet, wins, and rises to 3000.
Then he has drained rating from the bullet pool.

I hope you are aware that people can start from 400 here as well. Of course, some people may start from 1 600, so there will be overrated people at the start, but there will be people a lot stronger than 400 who starts from that rating as well.

As for GMs stealing other people's rating... yeah that is how it works I think. Hikaru steals rating from Naroditsky, he steals from an IM, IM steals from CMs and NMs, who steal from strong unrated players, who in turn prey on the rest ...