I think most of the the problems would come from terrain, and the halving of movement values that comes with damage.
Moving across the board in two turns, in a more “modern”4*6 game seems kinda weird.
I have played a few games with both halved and full movement/ranges.
The full size games go a bit faster, as you can start shooting at long range turn 1 or 2 depending on terrain. It’s also harder to get in behind mechs who have already moved with mid speed mechs; although, by the halving of ranges, you already have to be a bit closer to be in weapons range, so they mostly cancel each other out.
It won’t come up super often but by halving movement you will end up with fractional inches once you take movement crits, which could be annoying, and could cause problems with terrain interactions.
Halving the distance for woods/terrain movement penalties to apply is another thing to think about, but not a big issue if you have a cheat sheet. Although it makes it so smaller terrain has a larger impact as it’s only 3” of woods to be concealed, so that sort of terrain needs to be either reduced in size or know you can’t fight through much woods at all anymore.
I think for hills in RAW you can only jump over terrain equal to half the Jump movement in inches high. To keep it the same, and effectively ignore that taller hills/buildings are impassable I’d say they can jump equal to their jump value inches high. Otherwise you’d have to rescale buildings/hills. That’s really the only pressing ‘problem’ with halving and keeping the terrain the same.