What if you could request kits from the trucks? Not anything like Angry Farmer Kit, just like a PR-style system, just... different. Operation Peacekeeper uses a similar system that involves supply crates or SL. You could also get alternate kits (the ones that aren't spawn kits, are limited and found on map.)
Example: A freshly spawn Opel is at monastery after Fallschirmjager finally cleared it out. You accidently spawned with an entirely different kit than you wanted because of a simple slip of your mouse, and none of the kits inside the buildings will do. So you walk up to the Opel, hold T, and request a normal AT kit with 3kg explosives (theoretically what you wanted) instead of your existing sad little Rifleman kit you don't need because of the 2 Vickers tanks attacking.
I also like the supply truck idea. Maybe all trucks could drop one ammo crate and ammo truck would drop commander supply crate? Not sure. Said ammo crates would only resupply infantry, but suppy trucks would resupply tanks and emplacements as well as repair?
After all, ammo trucks are mostly used as a quick ride rather than a team-essential tool.
(Well, except the occasional use to resupply arty, such as on Volpelldorf or whatever it is where arty has no ammo kit spawning near it.