Yeah, I think the goal of a rating system is usually more complicated than just "predict the next match result". Rating systems also serve as a way of rewarding past match results (not the same thing). And serve as an incentive structure.
Like, to give an example - say you retire from a match with injury. Does that mean your rating system should immediately drop precipitously? After all, you're injured, so if you played a match you would lose to nearly everyone. Therefore, if the goal of a rating system is to represent your current level, injury should immediately drop it to nearly zero, then recovering to something just below your previous level as you recover.
Or, surfaces! If a rating system's only goal was to predict match results, then obviously for the pros, their rating should suddenly change after Miami/IW (as they all switch to clay) and switch around after RG to grass-court predictions for a few weeks, then switch back to hardcourts. ...but that too would be dumb, because we're not looking for a rating system to be predictive - we're looking for it to judge how players already did.
(Imagine that rationale. "Yep, #2 player just beat the #1 player, he's had better results and is playing great... but his upcoming schedule says he's playing on clay, so he's predicted to play worse! Maybe, fellow commentator, he should announce his entry to some hardcourt tournaments, so the rating system keeps predicting his hardcourt ability and gets him to #1?)
...a lot of what rating systems do seems to me to make sense from looking at what their real goal is. And it's usually not JUST "predicting match results".
USTA NTRP has, as best I can tell, the goal of facilitating league play by grouping players into roughly-similar skill bands. I think that drives a lot of the decisions.
Why is there a single rating for singles and doubles, even though players might have substantially more skill in one than the other? Because once a player is on a team the captain should be able to schedule them for any line, it would be such a headache if captains had some players that were eligible to play singles only and others that were able to play doubles only.
Why is the rating only updated (publicly) yearly? Because captains need to be able to make teams and then expect them to stay together for the whole season (where "the season" can vary in times across the country).
Why does the USTA take into account game differential and not just total result? Because the rating system needs to mostly work for rec players that play as few as 3 rated matches a year. If they only used final W/L, the rating system would adjust far too slowly for those players. (Why doesn't USTA require more matches? Because they don't think these ratings really serve as a usable incentive for most players, if they required more matches they expect most of the impacted players would just go "shucks, guess I'm unrated" instead of playing more matches to get a rating.)
Why does USTA treat new players the way they do, with self-rates and strikes and bumps? Because they want it to be possible for a new player to join a league and get a rating by playing in the league, rather than making a rating a prerequisite for joining a league.
Why does the USTA have this dynamic rating... and then yearly they do some weird adjustments to it based on a very small (relatively) number of matches at sectionals/nationals? Because they want nationals to work, with teams from different areas all playing together, so it's quite important for them to adjust whole areas to be rated similarly, and they can't do that during the year when players from different areas aren't playing each other.
And yes, all those constraints happen against the background of "the rating should represent the player's skill level, the higher rated players should win more often". But predicting match results is not the ONLY goal of the rating system, by far.
I think I understand USTA NTRP pretty well, including the incentives and why it's designed the way it is. I don't know the math - I think Schemke does - but I'm pretty sure I got the basic idea of how it works and why it is the way it is.
...I can't have the same confidence for UTR. Both because it seems more complicated under the hood, but also because I don't know their goals as well. My impression - despite the fact that they call themselves universal - is that the main goal of UTR is to support recruiting of pre-college juniors. They feel they have enough market power in that area that they can dictate to their players that they need some minimum number of match results, so they don't have the USTA's issue where they have to have good ratings for players who only play 3-4 matches. They do not care about extremely imbalanced pairings like USTA Mixed Doubles because that just doesn't come up routinely in junior play, it's a quirk of the USTA's gender-segregated mixed doubles leagues. They seem to care a HUGE amount about their rating sytem being EXTREMELY responsive - juniors can change fast in skill, and if someone goes through a huge skill leap in September they want that to be represented in their rating ASAP before college recruiters make their decisions, even if that takes silly hacks like players' ratings being retroactive and causing recalculations.