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I always thought it'd be neat if HM Moves weren't really removed, but rather if HM skills weren't just limited to a single move.
For example in addition to Cut,
>Slash, Cross Poison, Night Slash, Psycho Cut
>False Swipe
>Aerial Ace, Wing Attack, Air Cutter
>pretty much every Fire move
etc. could cut down the little trees. You could do something for pretty much every other HM move too (ex: Pokemon who know Aqua Jet, Dive, Muddy Water, Waterfall, Whirpool, etc. can Surf in the overworld)