Maybe a long time ago, I've lived here 15 years and there's not been one

Other than the ADA compliance mentioned, there's also weird property ownership and utility access things that can come up.
The laws that give them the ability to put sidewalks on your property usually phrase a limit on where they can put it. They can't just cut a 45° corner off your lawn because it's easier. If the property that owns that wall technically exists in a funny shape their sketches of the plan could have happily breezed along making a weird gap.
There could also be a utility junction under that area that they didn't want to cover.

I don't think there was a tree because you don't see the mound or divot that you usually see if there was a tree somewhere, at least one big enough to warrant that much of a sidewalk swerve.

Anything weird like this is usually to meet ADA requirements for wheelchairs.

Can only have so much slope each way.

Because some designer said so. Doesn’t have to be a reason other than “I think we’ll bend this here towards the crosswalk.”

There were concepts of a plan to plant one.

Because there’s a ramp on the left side of the image that leads somewhere, like a crosswalk!