Interesting, can you share a few OSM links of POI that use old_name (and are disused)? I’d like to understand how they get rendered, if that’s really the better approach.
I tried to use Nominatim to search for disused:tourism places around me (London, UK) but I couldn’t see any.
A quick check on disused | Keys | OpenStreetMap Taginfo shows that less than 10% of the disused values seem to use it as a lyfecicle prefix (the rest use the discouraged “disused=yes” or =no approach)
Use of disused=yes is discouraged for features like shops, roads, parks or museums. See the namespace prefix disused:= instead, for example disused:amenity=, disused:leisure=, disused:tourism=*.