Parker draws so much attention that our complementary role players can afford to be a little bit "sloppy," in a sense, when making plays off the ball.
Our secondary ball handlers are quite a bit more inferior/ineffective compared to Tony in terms facilitating (Manu, De Colo, Mills, Neal, you name it) which leaves far less wiggle room for our other guys playing off the ball.
Without Tony, you have to set cleaner screens, your positioning on the roll (off a pick and roll) has to be more optimal, your timing on passes has to be a little bit more crisp because the defense isn't nearly as worried of De Colo or Neal with the ball versus Tony Parker.
I mean this is all speculation of course, but it feels almost miraculous when De Colo, for example, successfully assists against a competent defense, given that he's such a non-threat to score. The timing/precision of his passes has to be absolutely on point.