I’d expect that with more feature tags (aka top level tags) for paths there would be a similar amount of disagreement, but it would be less consequential.
For classifying motor vehicle roads we have 7 main feature tags—21 feature tags total with special road types and link roads included. (See: Key:highway - OpenStreetMap Wiki) Disagreement over road classification is common, but it’s usually over small adjustments within the classification scale. I.e. one mapper thinks a road should be highway=unclassified and the other thinks highway=tertiary. We’re generally not seeing disagreements where one person is arguing for highway=primary and the other is arguing for highway=service.
I’m very glad we don’t just have one feature tag for all roads from motorways to driveways. This would lead to big disagreements over how data consumers ought to interpret it. Some people would say they should assume nothing and rely entirely on property tags like width, maxspeed, surface, lanes, etc. Others would point out the large number of roads mapped without any of those tags and the data consumers that don’t support them. It would be a mess. The current system at least means that a road mapped with just one highway=* tag and nothing else gets interpreted in a somewhat reasonable way by most data consumers. It’s not perfect and adding property tags is good, but no one is arguing about driveways and motorways looking exactly the same on a bunch of OSM based maps and that’s generally a good thing.