We tried to set boundaries around screen time, but my daughter broke her leg between 2 and 3. It was above the knee so she was completely immobilized for 12 weeks. We allowed unlimited screen time and a couple awesome things happened:
I found out she has a natural gift for video games (vis a vis the switch).
She's 4 now and mostly regulates herself. If she wants to play, she plays. If she wants to play with me and I suggest mario kart, she says "no daddyyyyyyy, I want to play ball catch (or whatever other thing she wants to do that is absolutely not what I want to do which is relax and play a video game.)
ETA: regulating sweets are a bigger problem for us.
Also, yo Gabba Gabba re-runs on youtube.