I'd rather have weapon powers than weapon skills and weapon restrictions.
Rather than have the heavy weapon skill, I'd rather have an ability that increases AoE and range of heavy weapons.
Rather than have the sniper rifle skill, I'd rather have an ability that doubles the effective range of a sniper rifle.
Rather than have the assault rifle skill, I'd rather have overkill.
Rather than have the shotgun skill, I'd rather have a huge AoE projectile at close range (similar to ME 1 carnage but a lot more damage)
Rather than have the SMG skill, I'd rather have a skill to reduce recoil and improve accuracy (similar to ME 3 marksman)
Rather than have the heavy pistol skill, I'd rather have a skill to increase penetration and damage of heavy pistols.
All classes will have access to all weapons and be able to use them effectively.
However certain classes would excel with certain weapons better than others.
For example the Adept would be fairly decent with an assault rifle.
However the soldier would excel with an assault rifle.
The sentinel would be reasonably proficient with sniper rifles.
However the infiltrator would be a master when it comes to sniper rifles.