Could the heavy armors have a penalty to strategic and tactical movement, and the light armors have a bonus?

(This may have been mentioned before, but I think if lighter armors could move further and heavy armors have a penalty to movement, ie. lower strategic movement and a higher AP cost for tactical movement, this could provide a cool partial counterbalance to the "always get the heaviest armor you can afford" problem.)

Along with some minor but influential changes to the way armor works in combat, this could be a really cool feature for the game.

After all, how many games have heavy armor wearing units move at the same speed as lighter armored units, and have armor negating all damage?

Best regards,
Steven.

PS: As an aside, I think it would be better if high level magical equipment (especially armor) had a prerequisite of high level mundane equipment too, so you couldn't just rush Magic and avoid the need for mundane equipment.