Why would it be illegal to enter on yellow? I thought that's the entire point of yellow. Otherwise we'd just have red and green, and hopefully you can imagine how that would work out.

In some states you are supposed to attempt to stop on yellow unless it’s unsafe to do so: https://axleaddict.com/safety/The-Meaning-of-the-Yellow-Traf...

Its the leaving on red being legal thats the interesting part.

Plenty other jurisdictions will ticket if your car is still on the intersection when it turns red.