Many cyclists do ride on public roads for fitness reasons. Beginners might ride in local parks or smth, but I'm pretty sure most of the cycling hours are spent on the roads. Since people who ride more put in significantly more hours and tend to ride roads more. There's offroad cycling, but in many cases it involves cycling on unpaved public roads or other public areas not reserved to bikes only.
I myself spend more hours on public roads on a bicycle than driving a car.
In my personal and not so humble opinion, you shouldn't ride on public roads for fitness reasons. If you need to get from A to B, like from home to work, and you want to do it on a bike, fine. If you want to add some fitness routine to it, it's fine too (your lungs would probably disagree) - but you have to focus primarily on staying safe and not endangering others.
But pure sports? There are parks for that.
Don't get me wrong, I'm all for reclaiming cities for pedestrian and bike travel and creating a maximally energy-efficient public transport system (ironically, the best idea would probably be self-driving, publicly-owned electric cars forming a PRT network). But in current situation one has to stay pragmatic.
There are parks? Where exactly? Riding anywhere but on the road is dangerous. Most reasonably fit road bike cyclist can average 18-19 mph and possibly much faster on a slight declines.
We should be promoting cycling not making it even more difficult. Self driving cars can make cyclist significantly safer for everyone. The most dangerous thing on the roads right now is human controlled cars.
If I'd do "pure sports" at parks, many parents with children would be not so happy about that.
I love to go on long bike rides. Like 4 or 10 hours long. Parks is not an option for that. While backroads are awesome. Once out of town, I usually meet a car once in a while. And while in town and suburbia, I guess I can qualify as A to B commuter. Even out of town, sometimes it's sort of A to B commute, because I want to go to some sightseeing spot or fancy cafe in the woods or smth. I just happen to cycle instead of drive. Or sometimes I dispatch my family in a car and go by bicycle myself. It's still A-to-B, isn't it?
Saying what is and what is not a "proper road use" is a very slippery slope. Is it OK to drive to get to a grocery store? Is it OK to drive to some spot in the middle of nowhere for sightseeing? Is it OK to drive for few hours to bbq in an unseen place? Is it OK to drive to go fishing in a nicer lake instead of the one nearby? Is it OK to drive to see friends if you can video call them instead?
You want pragmatism, but what you're giving cyclists is the exact opposite of a pragmatic situation. Cyclists are being extremely pragmatic when they cycle on regular roads...
I myself spend more hours on public roads on a bicycle than driving a car.