I do not have anything against having to get out of vehicle and rearm it "by hand", but it gets very tedious as you can't pick up most of the vehicle ammo unless you have a backpack (which you don't most of the time since those are only found in HQ and harbors at the moment). I am not so sure how correct it is to require vehicle crews to have huge backpacks, realistically speaking.
This currently applies to resupplying a BTR with the 14.5x114mm ammo, I did not have the opportunity to rearm a Humvee, I imagine it has a similar issue, but it depends on it's ammo weight.
Example:
Rearming a BTR in Conflict game mode:
1) Open ammo crate at any Armory
2) Try to take the ammo
3) It's too heavy, even if you put away all your weapons
Workaround#1: Have a completely empty backpack, put one crate of ammo in backpack, then board the vehicle as gunner, press tab, put ammo from backpack to turret. You have to do this several times repeatedly because the turren storage is not accessible from outside of the vehicle.
Workaround#2: Press tab when close to the ammo crate, open the ammo crate, drag the ammo onto the "Vicinity" title on top of inventory window. This is not intuitive at all, and given that sometimes it does not work immediately (lag?) you may even think it's not working, as there is no visible feedback it moved the ammo. This took me a good 10minutes of fiddling with the inventory to figure out. On top of this this only puts the ammo into the trunk, you then have to transfer it into the turret by entering the vehicle, pressing tab and fiddling with the inventory again.
Possible Solution #1: In Conflict gamemode: make backpacks more available (at normal bases). Other game modes: crew needs backpacks. However I think this might only be a temporary solution depending on how heavy ammo for Tanks and Helicopters will be in the future - those may not even fit the backpack weight. Vehicle crew with big backpacks look weird though.
Possible Solution #2: Have a way to move ammo directly from ammo crate into the vehicle. Using the existing inventory system - for example by allowing to open vehicle inventory instead of personal inventory on the right side. Or by allowing to carry individual vehicle ammo boxes in hands (unable to use weapons unless dropped) physically - most immersive but probably requires more work.