I feel bonus move may be better as a support perk, if this was implemented. I know I certainly would be highly hesitant to take it as a level perk.
Perhaps needing of a 9 in agility to take. Maybe in Klamath or in NCR. Would be commonly grabbed, not a huge advantage. At the same time, it'd bring out redundancy since there'd be no advantage for anyone other than speed boost.
Also, it'd free up a perk for TBers, which is debatable if that's a good thing.
I'm on the fence, redundant, but wouldn't really be opposed to it as a support perk. Level perk, since I'm an RT player, I wouldn't want to grab it. I'd want to use that perk slot for other perks.
However, I also like the idea of moving a bit faster.