I’m no publisher of HHGTTG (nor artist as you can tell), but I’ve always imagined it somewhere along the lines of this:
Yes, it probably would (or using other style as default; I don’t think OSM is married to Carto 'till the death tears them apart; or at least it shouldn’t be). In any case, people would still first need to agree that change like is good idea and something they want.
Sure, but I’ve suggested exactly two (relatively simple) ideas pertaining to default OSM style, not everything…
Carto did recently implement different rendering for different surface tags on highway=residential/primary/secondary/..., so it is not unimaginable that they might add separate rendering for missing surface on highway=path, if community thinks it is a good idea.
The other idea of rendering ??? if there is no name nor noname=yes tags also doesn’t seem so hard to implement, or so objectionable (to me).
But the main question before proceeding is “do people think those are good ideas?”, or at least “do they object vehemently or not?” 
I don’t think something like overpass turbo would scale at all (not unless we have pre-rendered vector map style implemented first and style that instead; which is great idea in itself if you ask me - see Add OpenMapTiles vector map by zdila · Pull Request #4042 · openstreetmap/openstreetmap-website · GitHub, and it opens a lot of other possibilities)