That's seems unnecessarily confusing. Why even bother with the red arrow at all then? I guess it could be useful in cases where the straight-through traffic is green, but you want right-turning traffic to stop before turning, but is that common? Or even a useful thing? Like, I feel like if you've set things up that way, maybe the intersection is just designed poorly.

It is definitely confusing. In Washington state, right red arrow does not prohibit turning on red. I learned this after people started beeping at me to go at such an intersection. And yes, that intersection (Queen Anne and Mercer in Seattle) is confusing and poorly designed.

I don't think I've seen many intersections with red arrows unless there is a dedicated turn lane, where green yellow and red are all arrows. If it's a right turn in a right on red jurisdiction, without a sign expressing no right on red, why would red arrow be different than red circle?

MA allows right on red arrow after stop (absent a sign to the contrary). There are intersections where right on red is prohibited to protect a pedestrian walk phase that’s aligned with the green for straight ahead traffic.