Most of us have no time for the wiki ‘approval’ and voting process. It is run by a small coterie of wikifiddlers and has very little to do with whether tags are used or not; and nothing to do with consensus or democracy.
Instead we use tools like taginfo, tagwatch, and tagdoc to see how tags are actually used in practice. As of a couple of days ago the tag had the following usage in GB:
public_footpath (19062), public_bridleway (3143), restricted_byway (550), permissive_footpath (331), public_byway (211), byway_open_to_all_traffic (164), bridleway (103), permissive_bridleway (65), byway (58), footpath (57), ORPA (46), unknown_byway (32), quiet_lane (31), public_cycleway (29), site_of_special_scientific_interest (10), unclassified_highway (6), uncertain (5), LNR (4), British Grade II* (3), Civil Parish (3), Other Route with Public Access (3), undefined (3), British Grade II (3), country_park (3), public_bridalway (3), pedestrian_zone (2), Local Nature Reserve (2), unknown (2), national_park (2), Grade I listed (2), unofficial_path (2), former_permissive_path (2), unofficial_cyclepath (2), public_highway (2), Grade II (2), NNR (2), GB24A (1), public_bridleway;public_footpath (1), ORPA - higher rights uncertain (1), grade_II_listed (1), proposed_public_footpath (1), Scheduled Ancient Monument (1), permissive_bridleway;public_footpath (1), public_footpath; permissive_bridleway (1), not_highway (1), private_footpath (1), NSA (1), cycleway (1), common (1), ORPA; adopted (1)
I think nearly 20000 public footpaths so marked might be an indication that it is seriously in use.
As for technical solutions for mashing up your own needs: Maperitive pretty much does this out of the box. Download the area you are interested in (or use a Geofabrik download), write a simple Maperitive style sheet (or borrow one already in use), use it with the web map option for the background map and it’s easy to have a public footpath/bridleway/byway etc overlay.