I've thought about this idea a lot over the past.
I can see a lot of appeal to being a field-quartermaster so to speak, carrying spare mags and ammo for people that they can't carry themselves. You're lumbered down with more ammo for yourself and meant to be providing covering fire, you will almost always be following on so to speak, and so, if your team get themselves wiped, they can regroup with you after re-spawn, grab a few fresh mags and crack on. One particularly useful thing to carry is extra pyro, most vests only account for one or two grenades of any sort, three to four at most, I ALWAYS like to be fully stocked on things that go bang, if you have a team-box, people can just come grab as they need.
I've seen a lot of areas where this can be quite useful, longer, fiercer games where maybe all you need is a couple hundred more rounds to top you up after a drawn out, aggressive (and probably failed) assault and the safe zone keeps you out of play a little bit too long (picture this: respawn, take an extra two minutes to go to safe zone, only to find that the one guy who was holding out has been had and is now doing heading your way as you walk back into game)
That being said, how many airsoft teams, are organised enough to make use of it? How many milsim games allow you to carry extra rounds, let alone for other people or enough to make it useful? How practical is it to rely on someone who may often get left fairly alone to be your supply line? With your main job being suppressing fire and fire support, if you can take extra ammo, shouldn't you do so yourself? Real armed forces usually go with the rule, take as much ammo as possible for your weapon. If you have the space, should you do so yourself?
I'll let you decide on the practicality, I still like the idea myself.
I'd take a look at something like a rip off medic pouch, that way your team can literally pull them off your rig without you even moving, and you can do the same, even when lying down etc. They tend to be small though so you may have to look around see what you can find, though even a small one would probably fit a dozen or so medium sized speedloaders and a small gas-refill thing. Just stick three or four of those on your back.