> OSM not based on what you see on the ground?

Yes, but because of the rights of way laws in the UK defining RoWs as not necessarily the same as paths on the ground, the Definitive Map also has to be used to feed in to the OSM mapping.

Navigation apps should factor in the trail_visibility=no hint and ford=yes and weight their routing so it goes over the bridge rather than the ford.

In some cases, people have re-tagged historical footpaths (which are still legal rights of way) as disused:highway=footway, and kept the designation=public_footpath and foot=designated tagging.

I’m a bit hesitant about that here because there’s not going to be any physical sign of the ford across the Kent even if it’s commonly used. It’s a limestone-bedded river, so there will be no ruts in the riverbed. But if you’re certain the ford is completely out of use (rather than only occasionally used) then please go ahead and change the tagging to disused:highway=footway.