There is barrier, shield, health and armour. Not sure where the difference between barrier and shields really are gameplay-wise.
Barrier and Shields are basically the same, except one is purple and one is blue, at least in ME2 and ME3. In ME1 there was no distinction. There was a difference in powers that had multipliers to each one in ME2 and ME3.
You go on a mission, you have no idea how the enemy will be equipped. What do you take? If you could just swap ammo to match the enemy you won't need a bag of guns.
You can take what compliments your powers. If you have powers strong against shields, you would take weapons that are good against armor, or vice versa.
Gameplay-wise the gun should match your preferred range of combat. You go close you take SMG. Closer you take a shotgun. Want to snipe take a rifle.
There hasn't really been much tangible difference in ranges post ME1.
Looking back this would work fine in SP. However in MP you cannot switch ammo so that bag of weapons might be needed again, but then there is weight to consider if you're in for power casting. If you ditch the weight penalty everybody ends up using the Claymore anyway. Being able to switch ammo in any game mode might just add to the variety of weapon choices.
Well first of all it is unclear that the weight system will return, and I am not advocating for weight-cooldown interaction mechanics. Secondly, I don't know why you need to have ammos for protections since there are essentially only two protections. In ME2 essentially you were strong against armor (pistol, SR), strong against shields and barrier (SMG, SG), or decent against both (AR). Taking ME3 as an example, every single faction has some units with armor, and every single faction has units with shields/barriers. You can't guess wrong, you always run into those protections.
If you took ME3 and completely ditched weapon weight so every weapon had identical cooldowns, everyone wouldn't jump to Claymore anyway. There are too many guns that were overpowered. And in any case, this doesn't have much to do with differentiating weapon classes with multipliers.