I like it. There's always a replacement weapon or ammo to collect, there are Vigors to use, not to mention you can be highly mobile and use the environment to your advantage (making proper use of skyrails for example), and there is never a time when your weapon is 100% useless for the situation. Yeah, sure, a shotgun at long range is poor, but it can still kill if required, and there's likely a carbine or a sniper rifle or even a pistol somewhere nearby.
Since every weapon is effective in its own way, and there's always vigors to use, and Elizabeth often finds ammo and salts for you, I don't mind the limit. It makes me think more about what guns I should be carrying right now. It also means I have absolutely no problem with picking up and using the powerful weapons like the Crank Gun right away despite limited ammo, since I know I can always replace it with another still effective weapon.
Duke Nukem Forever is a prime example of weapon limits done wrong. I'd be ok with limits in that as well if not for the fact that half the weapons in the game were simply fun gimmicky weapons and weren't really effective at all. Why use the Shrink Ray? It's unreliable, it doesn't kill, and it has very limited ammo. Weapon limits means I can't carry it around and use on occasion just for fun, because its dead weight 90% of the time and I could use a better weapon. Despite requiring explosives for boss fights, it was never good to carry around an RPG or Devestator either, since they had very limited ammo, and boss fights always had these weapons and ammo for them strewn about everywhere. So why carry it when after like 4 shots its dead weight, and I'll be handed it on a silver platter just before a boss fight anyway?
With Infinite, I could kill a Handyman with a pistol, so it doesn't matter as much if I use up all my RPG ammo on a bunch of random soldiers. More room for fun, while also making you think more about your weapons, and getting you to use a larger variety of weapons.