A command action spent trying to fix a bad position or race to attain some desired ground, is a command action not spent on drawing a card or using a faction ability.
True, but if the mission is to obtain the strategic position, then you've dramatically changed the way the game works. (I'm not opposed to changing the game, but it must be demonstrably shown as a positive). And allowing people to fix a bad position is functionally taking that element of maneuver out of the game.
Beyond that being able to (functionally) run may not allow units to final rush, but it would let them final rush earlier. If I'm 8" away from an enemy, it does not matter that I get the +1 MC on the final rush or on the previous turn. This would let units run around the flanks on enemy units and get the pinch earlier, which would have a big impact on the game.
I see what you're trying to do: fix the Hawk Great Sword and Heavy Infantry. I get that. Even Chad said it was a bit of a problem. But the solution there is not to create a system-wide rule that fixes only 2 units. Because in fixing those 2, you've created problems elsewhere.
That being said, YMG is (understandably) reticent to make card errata and BGFW has what amounts to a living rulebook. So the least painful way is to fix it there. Given that, my suggestion would be to tweak your suggestion so its in the rules but functionally only affects the units you want.
One idea would be to allow your Run ability but only if the unit has a base move of 2.5" or less, and only if the unit starts further than 7" from any enemy unit. Units that do this can't make a Ranged attack. The fall out is that most units of artillery would be able to run like this. I dunno if this is okay, but I suppose I could live with artillery unlimbering and running. The other situation I can think of off the top of my head is that zombies could now run, which does seem a touch weird.
So in the end, it may be better to just live with Greatswords and Heavy Infantry.