Well, overcoming the limits/challanges is what makes the games fun. Restricting number of weapons makes designing easier and allows for more precise control of difficulty level. Same as with regenerating hp - designers had to design a level in such way that it wouldn't be too easy for someone with full hp, and that it would be passable for someone with 10hp left.
remember that most fps games are made for multiplayer too - you can't have bigass windows with 10 weapons to chose from in form of big circle menu.
try designing control scheme that fits gamepad and allows for most fps actions and lets player chose more than 4 weapons, seamlessly without any additional interface. And remember that most games aren't just run'n'gun - player has some special abilities at his disposal. Good luck.