I like this idea, it reminds me of WH40k. For those who don't know, one of the factions, the space marines, have heavy armor suits with an assortment of melee and ranged weapons (pretty close to MAXs in concept and execution, the standard infantry being close to HA level of armor and firepower), called Terminators, like this one :
(Note that this is a melee variant, the standard equipment is the equivalent of a dual rocket launcher on one arm and a super-powered fist on the other, and that the WH40k universe has always been quite keen on the whole melee thing)
As for the gameplay itself, I think it fills a certain niche in base assaults, if you need to take out a heavily dug in enemy force with lots of armor/MAX's in a confined space where standard heavy ordnance is too risky for friendly fire. Plus, they would be great for most MAX crashes, as you tend to end up pretty much in melee anyways, especially if the MAX's keep the sprint ability. Also, if we end up with an equipable knife (which, from what I can see of the community here, would be much better than the current quick knife), the MAX could use some slightly larger equivalent, even if it doesn't do more damage (if only for esthetic reasons, although I think having it do more damage, but with a slower equip/refire rate, would be a better fit).