There are many different types of filters and displays for many different reasons. I had like 100 buttons for preset filters and overlays for many situations.
We could also look at the raw analog data in real time on the right display or plot it afterwards with software. No AI is filtering things out by speed or other ways. There are pulse doppler filters and things like beaming a radar, which is a tactic. Even the recent balloons shot down weren't assessed as a real threat and don't compare at all to real threats and things we deal with like maneuvering, jamming and missiles that give you minutes to react. These balloons take days to even get somewhere.
We have people actively degrading radars both friendly, accidentally, and with intent. AI could probably help a lot in those situations but it's always a game of cat/mouse.