I cannot agree... bicycle tag is legal access to a path, not difficulty, here the table for routing:
osm.wiki/OSM_tags_for_routing/Access_restrictions#Italy
You should warn the router's author that his software should use that page as a reference for supported countries.
Putting bicycle=yes or any access tag is a repetition of defaults that makes heavier the database and doesn't give anything more.

Can you please tell what router? Usually they should assume the default when nothing specified. Please consider using: mtb:scale=* to help mountain bikers

It's the default in Italy, please don't add bicycle=yes to paths