I feel like he's taken a couple of moderately contested threes this season and hit them, which is really encouraging for his long-term prognosis. I think if the Spurs don't prioritize getting him the ball, he's not going to get looks. First, the book is out on Danny, so teams aren't going to leave him hope and second, Kawhi will never have Parker's gravity.
The latter case the Spurs have tried to remedy by having Danny be the entry-passer. It didn't work last year, but it's working well enough this year. If Danny is comfortable taking contested threes and hits them at a decent rate, that will help him and LMA a ton.
The former case will only be resolved with plays and actions that give him the ball. The plays are rare but have been working when they get to happen (except the corner Hammer, which has been well-scouted). The actions have been getting him open, but it's not ingrained in the offense to look for him at certain points. He's still being treated mostly as a bailout man or a way to exploit weak defense. There's no "Well at this point in this play, you know so and so is going to make a cut which will leave Danny open about half the time, so look for him then." contingency in their offense.