I also have a UC4, which does have a Live mode, which works as expected (at least on Live9). I.e. you don’t have to map anything, it’s all pre-mapped. You just have to install the files that come with it. It does lack the LEDs the SC4 has, and of course it’s not a dedicated device like the FT3.
I have times where I try to use it with live, but always end up using the mouse. There’s always going to be soo much that is not mapped, or not easily reachable, on the controller, so you keep bouncing back and forth between it and the mouse anyway.
This is for “sudio use”, for live stuff it’s a different thing, because there you set things up to work in a very specific way, and you don’t want to touch a mouse, at least I don’t.
For the latter I can see something like the UC4 to work fine. I would likely restrict everything to 8 tracks (or gropups) max, keep the UC4 for just track levels and mutes and perhaps add a second controller to control effects/sends and other parameters that need to be at reach.
Mapping these controllers to something is very quick&easy. You just enter MIDI mapping mode on live and turn a knob, push a button or move a fader. That’s it.
The tricky thing for me is then to remember what I had mapped, but that’s another topic.