>Why? IIRC if the mouse does also not spawn a new mouse event every frame even if it is not moved, right?

I'm not sure what you're trying to say there, but I can explain a bit more: Previously, the analog sticks were translated to button presses. Think of a mouse that would only send a single event "left" if you're moving it to the left and "up" when moving it back. That's not enough to do get the precise location of the mouse cursor, or the position of the analog stick. (It may be enough for mouse input as the cursor location usually only matters when clicking, but that's an optimization we cannot do for analog sticks.)

Now, every time the controller sends an updated stick position, the new position is sent to the script. If you don't move any sticks or triggers, no calls are made. However, the sensors are so sensitive that the position will even change slightly if you're just holding the controller in the hand without touching any of the sticks. If it turns out that we have too may events, we could introduce a "minimum movement" threshold.

>What about PS-like controllers?

This is mainly about the presence of buttons and sticks, not about the exact layout. For our purposes, a PS controller is the same thing. The only disadvantage you'll have with a PS controller is that the X/Y/A/B button labeling does not match. That's still better than the previous button numbering which matched neither the PS controller nor the Xbox controller.