Some of the “renderers” you’ve identified are merely sites that embed maps from providers that don’t give their customers the option to distinguish highway=road from highway=residential or highway=unclassified. Those tile providers would’ve been in a better position to respond to your inquiries, although to set expectations, few of them ever devote resources to following the OSM tagging debate du jour.
Even so, this proposal does have an undue emphasis on renderers. If the motivation is that highway=road can potentially represent a rugged walking path, then routing engines should be considered too. Most routing engines offer a walking or hiking profile. For example, OSRM’s default driving profile excludes highway=road but its default walking profile includes highway=road. Absent any changes, this proposal would effectively promote tagging that excludes pedestrians, seemingly contrary to your intention.
This was not a concern for previous proposals for new highway=* values, such as highway=busway, because there was an expectation that none of the “standard” modes of transportation should be routed along them by default.
How about some golf cart paths?