If the purpose of a firearm is to actually kill the enemy, heavier is better. If the purpose is to keep the enemy out of your line of fire, lighter is just as good.
Were it not for the logistical difficulties of having to deal with separate calibers, I would think it might be interesting to have a firearm with separate "suppressive fire" and "targeted fire" functions (probably two barrels, fed from separate magazines). I'm sure the weight and complexity would render the idea impractical, but there would be some appeal to the idea of having 100+ rounds of .22lr ready at hand.
I've also seen the argument that more, lighter rounds are better because a lighter round is more likely to wound or maim than kill outright. A dead soldier can't fight, but won't do anything to slow the rest of them down. A wounded soldier can't fight, and may force the enemy to expend time and resources taking care of him.
Several (OK, many) years ago there was a full auto .22 rimfire offered to police departments. A friend of mine had the repair contract on them and I at least got to look - and to see some of the techincal stuff.
A very high rate of .22 rimfire (the little guys) will tear big holes in just about anything. Problem is that you have to keep a high rate of sustained fire on the same point (bull's eye) 'till enough lead got there to do the job: easier said than done. And, yhe result at point of origin was sort of like the early days of rifle caliber gatlings in gunships - burned a LOT of ammo and made a real mess.
(I don't know if that has improved or not)
As to 'carry more rounds...", what I remember, from military and from watching SWAT teams on the news, was a whole lot of "close eyes - squeeze trigger - reload when the sound stops" marksmanship.
What I see today from Iraq looks like training has improved performance - but I havn't seen any video of down in the dirt gunfights.