That's the thing about March and the same as with Commando, one unit with it is not enough. You really need a whole stack with it. Otherwise, you can't make the progress with the stack that the promotions could enable.
If I do give anybody March, it's a stack defender unit. I want that guy healed as soon as possible. I sometimes think about giving March to Great General units, but again, they need to be protected by a healthy stack.
Absolutely the worst use of March is to put it on Infantry. The next upgrade -- to Mech Infantry -- gets March free with every purchase.