Is this score meant to be like a derivative of one's rank? How fast one's expected to climb from their current rank? Or, more like a game-agnostic aggregate ranking?
Really only winning matters at your current rank, other metrics can be deceiving.
For instance according to the tool my league account is D-tier in most metrics and gets an overall ~400/1000, except that it has a near 60% winrate over 200 games on my main role while playing against the top-5% of players in my region. As a toplaner I generally want to be on the opposite side of the map from the current objective and I'm not going to get to participate in many kills either - so my objective participation and kill participation are both D-tier. If I made improving those metrics my goal I'd be playing incorrectly and I'd likely lose more games.
In a shooter a high KDA in [current rank] is going to correlate better with winrate, since killing your opponent is the main avenue to victory, however you could still imagine a hypothetical player who gets a lot of kills but makes the game so hard for the rest of their team, they lose anyways.
At the end of the day, only your current winrate is a reliable metric for how fast you're going to climb from your current rank.
Scoring for League presents several challenges as you mentioned, and I’m not particularly happy with the state of our League rating. In theory top should still be picking up standing objectives, which are accounted for, but yes KP will be lower for top. The goal is to use stats which can work for all roles but of course that is particularly challenging for support and top.
