There is a massive difference in the role of coaches for high level players and lower or mid level players. The key to improving at chess for lower level players, and the very thing that means almost none do to any significant degree, is lots and lots of work that isn't necessarily that exciting. For instance tactical exercises where you analyze a position and determine a winning (or drawing) sequence are absolutely critical. Every very strong player is going to have done tens of thousands of these exercises. Even Kasparov at his peak would regularly solve studies each morning with his breakfast.

There are many sites for doing this work online including lichess.org, chess.com, and then specialized sites like chess.emrald.net, chesstempo.com, and others. However, in my opinion they are also mostly useless. The reason is that interactive solving creates a practically irresistible urge to just try your move once you find one that looks correct. In general in tactical problems, stronger players are going to be able to reduce a position down to one or two "candidate moves" (moves that might be the 'right' move) and so the odds of success by guessing are incredibly high. In poorly designed tactical problems, as many of these sites host, it's sometimes the case that there's only one real candidate move - or that all of the candidate moves are good.

Those sites also suffer from the problem in that the defense offered is often weak. They generally use computers to solve the problems. So imagine we have a position where you make one kind of obvious sacrifice to initiate a tactical combination. The computer sees that if accepts the sacrifice then it gets mated in 7 moves after a series of highly complex follow ups. So instead it gives away its queen on the first move to stave off immediate mate, and the problem is "solved." That's quite ridiculous.

The real key to tactics is to work them out in your head, in entirety with all possible defenses, and the and only then finally commit. Only sites are currently just not very good for this.

Aside from the unwillingness to do the actual work for improvement (tactics alone can take players practically all the way to FM strength, which is about 2300 ELO) there's another big issue. Players are obsessed with openings. A datum I read once indicated that more books had been written about chess than any other sport or game, and I'd estimate 95% of those books are going to be books on openings targeting beginner to intermediate players. Openings are mostly irrelevant in chess. If a stronger player plays 1. a4 (a completely awful opening) against a player just 100 points below him, he's still going to be a clear favorite. Nonetheless players spend their time obsessing over openings. The reason is because unlike tactics, it "feels", like you're learning something.

Chess improvement is very weird. It's often a star step inside of an upward slope. What I mean is that you hit a level, get stuck there, study for months, see no improvement. Then you wake up one day, and are suddenly 200 points stronger. It's surreal. You can even see this in players like Magnus Carlsen. In April 2004, at the peak of his 'wunderkind' developmental acceleration period, Magnus was 2552. More than a year later in July 2005, he was 2528. 15 months of doing nothing but seeing your rating do nothing but decline? Nope, you haven't hit your plateau or some level you magically can't get beyond because of your IQ (a common excuse) or anything even close to it. That's just chess improvement for you.

Chess openings by contrast enable players to feel like they're learning. You'll, on occasion, even be able to win an entire game without ever leaving your preparation. But the paradox there is that it will generally have minimal to no effect on your overall rating or performance.

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As for high level players, most of what I just said is completely different. Since this post is already getting too long, I'll try to keep it short. Very strong players capable of converting very small edges. And so things like incredible nuance and openings start to play a very major part of the game. And so the role of a coach, or second, for a professional player is very much different than it is for a lower rated player. It's kind of the difference of a grade school teacher compared to a post-grad research partner. And you'll often find very strong players taking on much weaker seconds. It's not so much about their skill, but their knowledge and ability to discover new knowledge.