The MUP's are pretty tame in my locale. One that was originally named "southwest commuter path" is now just "southwest path" Even on the most busy days, the traffic just isn't extreme, and if it is, then I slow down. After one or two rides it's easy to recognize the stretches where you can really open up. The paths turn to gravel after a couple miles out of town, and the roadies take to the roads at that point.
Closer to downtown, they can get pretty busy. Riding through the college neighborhood on football game day, might as well walk the bike. The stretch that's along the lakefront, well, that's really a pedestrian area anyway, has a separate marked bike lane, and folks are generally cool about it.
It gets more crowded in nicer weather. That's a benefit of riding in crappy weather
Perhaps my main annoyance is that I'll slow down behind some slow riders or pedestrians while someone is coming the other way, and someone will blow past me and in between everybody without even announcing.