I don't understand the objection to team shooting efficiency. You claimed that TS% does not correlate with winning. I showed that at a team level it does correlate with winning. Team shooting efficiency correlates with team winning percentage; individual shooting efficiency contributes to team shooting efficiency. I don't see the objection.
Anyway, TS% is most decidedly NOT a "mush stat". PER - now that's a mush stat. But TS% is points scored per 2 possessions used. That's it. (The "2" is presumably in there to make things look kind of like FG% but it doesn't actually do anything.)
Points scored per possession used. That's shooting efficiency, and it's about as empirical as you can get. It's no less empirical than shots made per shots taken (FG%), and in addition, it accounts for the facts that 1) not all shots are worth the same number of points, and 2) not all points are scored on what is credited as a FGA in the box score. FG% is a good stat to measure scoring efficiency, eFG% is a slightly better stat to measure scoring efficiency, and TS% is basically as good as you can get in measuring scoring efficiency without trying to get all fancy and mush things up in the way that you don't like.
In other words, from a quality standpoint FG% < eFG% < TS%. All of these measure the same thing - scoring efficiency - and they should be used in the same general way, with the same caveats. The guys sitting at the top of the leaderboard on FG% are more or less the same guys sitting on the top of the TS% boards (yep, James Nunnally and his sparkling 2-3 on the season, too). If someone says, "A is a better shooter than B, look at their FG%" nobody blinks an eye, but if someone says "A is a more efficient scorer than B, look at their TS%" then they get dumped on. Makes no sense.
This is a bit like somebody telling you that a hamburger has 2.2 ounces of vegetable matter in it, and that therefore that tells them more than you know when you know the hamburger has 3 slices of onion, 2 slices of lettuce, and 1 slice of tomato. Even worse yet when the hamburger having 2.2 ounces of vegetable matter is often held out as having flat superiority over a hamburger having 1.8 ounces of vegetable matter. I can't deny that a measure of the ounces of vegetable matter in a burger does in fact measure the amount of vegetable matter in a burger, but I can certainly argue relevance, especially for my brother who hates tomato, or for a triple decker w/cheese heart attack burger that dispense with vegetable matter altogether in exchange for guiltier pleasures.
Three GMs go to make a trade. This is the information each of them has in front of them:
GM 1: Advanced Metric Boy
Player A: 58.8% TS%
Player B: 58.7% TS%
GM 2: Real Stat Man
Player A: 56.7 FG% (on 14.5 att/gm), 36.4 3pt% (on 0.4 att/gm), 68.2 FT% (on 2.9 att/gm)
Player B: 44.4 FG% (on 10.6 att/gm), 39.3 3pt% (on 5.3 att/gm), 82.7 FT% (on 3.0 att/gm)
I submit to you that GM2 knows FAR more about those two players. In fact those numbers are revealing enough that you can probably come up with a semi accurate description of their respective games without even knowing who they are/watching the games. With a FG% that high, on that number of attempts, no three pointers, and a shaky FT% on very few attempts, Player A almost certainly has to be a midrange or extended post big man of the Al Jeffereson class. With 50% of his shots coming as threes, and few FTs, Player B is certainly a three point bombing perimeter specialist. And yet TS% will tell you they are identical. Great stat.
I further submit to you:
Gm3: Actually watches the damn games guy:
thinks Player C: 54.9% TS% , is a better offensive player than either.
TS% is the exact opposite of an "advanced" stat. It obscures, not clarifies. Blurs together semi-related concepts, rather than sharpens the focus. You cannot deny TS% does in fact measure some overall measure of scoring efficiency. You can certainly argue the relevance of that particular piece of information on an individual basis.
P.S. Player A: Horford; Player B: Meeks; Player C: Cousins