This would be a lot worse than the current highway classification.
Neighbouring countries can have great differences in admin_level classification. I just have to look at the front door :-) See Admin_level, boundary naming on OSM.org and translation - #6 by Vinzenz_Mai.
In France the next level below national highways are on the admin_level=6, the departments. Roads where the department is responsible can be anything from trunk to tertiary, but there is very little difference between highway classification in France and Germany at the French-German border. I looked at all cross-border roads (not tracks or pathes) between the tri-border area near Schengen and the Rhine. In just one case the classification differs: tertiary → unclassified between Ober- and Niedergailbach (Way: Rue de l'Europe (373991358) | OpenStreetMap and Way: Obergailbacher Straße (30741429) | OpenStreetMap)
You will find the official classification (in France and Germany) typically in the ref. There’s a really big difference between the forementioned D 34a and the D 620 just around the corner, with a part as highway=trunk with motorroad=yes …
I don’t see how your proposal will get better results as the current tagging.
With cycling it’s even worse, please have a look at the discussion Bike route networks classification (ICN, NCN, RCN and LCN) - and no: the result of claude.ai in the topic starting was simply wrong :D Don’t forget that icn, ncn, rcn, lcn is most times tagged at relations not ways …
And then there’s this discussion: Cycling infrastructure between towns