I think it's a really interesting suggestion, but in my opinion it's too much of an ideological request rather than being a realistic one.
Surely, it is great to have scoring that is mostly dependant by skill, but scoring as it is now already reflects skill quite a bit. It's indeed a bit flawed since it's too dependent on your performance at specific times rather than overall performance, e.g. hitting a handful of 100's at the end of a big combo will lower your score more than when hitting a handful earlier when your combo is still in the double digits, while overall your performance is still the same. But those flaws are quite minor and if you look at the bigger picture, better scores are harder to achieve than worse scores.
Also, having four different scoreboards for individual stats wouldn't be much of an addition, since they would already be heavily determined by the style of the map itself. Hence the current scoreboard already tells a lot about a player's capabilities if you're interested and motivated enough to look into a player's abilities.
2. If pp were ever to update its calculations, it could affect (possibly significantly) the placement of scores on the leaderboards. However, as far as I know, no significant changes have been made to either tp or pp in a long time, so I don't think this would be too much of an issue.
PP is actually updated quite regularly and not as consistent as score is, considering the scoring algorithm is updated practically never. It's indeed not much of an issue, but it can make scoreboards fluctuate too much and rankings would become less solid and therefore less reliable because the score you set today might change over the course of time.
You assume you're going to SS the map, and start with the maximum pp the map can give you with the active mods. As your accuracy gets worse, it scales down the pp score accordingly, same for misses. As for combo breaks, you subtract your combo from the current highest achievable combo (which is FC at the start of the map), and the pp score considers the highest between the two. Missed slider ends just subtract one from the current highest achievable combo.
It would also have a major impact on gameplay. Right now, as you play the song you can watch your score increase and it can be a satisfying thing to see. Once you get to the point where overall performance starts playing a significant role, you'll get bothered a lot by breaking combos and seeing your shitty accuracy after going ham with 100's on a long stream. Seeing those is already demotivating, and to many of us a reason to hit the retry button for a better attempt right away. Imagining seeing the possible max pp all the time and the only thing it will do is decrease, and you'll constantly have the shitty feeling of not being able to get the highest possible amount of pp when you actually played the song quite well.
The most significant change that this would bring that I am interested in is the fact that your highest pp rewarding score would be taken into account, rather than the score with the highest actual score. Meaning getting a good score with DT when you already have a 99% FC no-mod score, would actually become an interesting thing to do, as right now it would net you absolutely nothing.
