This. 100% this. The county highways around where I live have a paved shoulder that is as wide as a full lane of traffic. I routinely cycle on that shoulder safely with cars zipping by me at 55-60 mph and no one gets angry about it.
But I do run into the bottom 1% of drivers occasionally (usually at intersections) who either simply do not see me, despite the fact I'm wearing fire-engine red kit and have flashing headlamp and taillight in broad daylight, or choose to ignore that I'm there and intentionally put me in danger.
There are a couple of longer-distance high-quality road cycling trails around here (one is ~50 miles long, the other is ~120 miles long) but they are an inconvenient distance away. The other park-style trails around here simply aren't meant for road cyclists, for reasons that you've noted already.
Of the clutter can be insane, there is a new, 3 meter wide path, and some donkeyballs-brained perdon has installed a lamppost, a large metal 'internet box', and some other metal box duagonally across the path, so you can't cycle through it any more, and get through on a wheelchair!
Not in terms of infrastructure. A mistake that planners often seem to make is to build "cycle lanes" that resemble footpaths: lots of zig-zags, stops and starts, clutter, obstacles to manoeuvre around, and diversions at junctions that make cyclists take longer routes than cars and force them to give way to all other traffic.
The best bike lanes resemble motor traffic lanes: straight and continuous with as few interruptions as possible.
If you build bad cycle lanes, most cyclists just won't use them and you haven't really solved anything.