Like many others, I too think of giving some utility to Cut, Razor Wind and many others. Sometimes, it is fitting to simply change their types. Other times, it would be better to simply re-imagine their mechanics.
I see suggestions in favour of turning Cut into Grass, Steel or Bug type. I confess that Steel did not occur to me, and I quite like these changes.
What I have been thinking, though, is to keep it a Normal-type move, but give it an effect that makes it super-effective against Grass-type Pokémon, much like Freeze Dry has its own effect that makes it super-effective against Water, whereas it should not be, under normal circumstances.
Alternatively, just remove Cut. Instead, allow Fury Cutter to do its part in the overworld.
I would also like to hear your takes on making Physical, Normal-type contact moves be type-fluid. If a Geodude uses Tackle, it would be a Rock Tackle. If a Steelix uses Headbutt, it would basically be Iron Head. It could be hard to define the limits of what makes sense (and what is balanced) with this mechanic, though.