No, this would make the game more like CoD and less like Battlefield.
The first thing they should look at is normalizing the resupply speed across all gadgets. Rockets for engis resupply in what, about 5 seconds? But EX40mm takes 15 seconds or so? That's 3x the time cost for not even a quarter of the utility. Smoke and incen cost about the same time.
Second, I'd put static resupply crates on OBJs, or at least at certain points on the maps. Most supports never drop ammo unless they're giving it to themselves, so relying on the team to get ammo usually sucks. Personally, I think there should be a point deduction for not giving ammo when you can to players spamming "NEED AMMO" right next to you, but ah.
To explain my first comment as well, Battlefield should have periods of slow play. It's one of the things that made it so much better than CoD. Having to stop sprinting for two seconds and taking a break to resupply seems to anger this new generation.