Turn 5E into hyperkinetic GURPS, you mean? That's a good approach, but it has two (minor) issues:
(1) It doubles the duration of spells in combat.
(2) It's a linear transformation which makes walking humans way too fast (7 mph), horses about right (27 mph), and dragons (36 mph) and giant eagles (27 mph) too slow--they should be able to go up to about 80 mph at least. (Compare speeds here:
https://en.wikipedia.org/wiki/List_of_birds_by_flight_speed)
Since walking speeds are by far the most common in D&D, I'm not sure that applying a linear doubling as you suggest is the way to go. It's an interesting idea to explore though.