My favorite gun in BioShock is the shotgun. It has a nice kick to it, it is very satisfying to use, and I appreciate that its spread means I don't have to aim very well. The more I use it the more comfortable I get with it, and thus the more I use it. This increasing preference-for/reliance-on a single gun poses a couple problems from a game design standpoint.
First, as I'm only using 1 weapon I'm not getting the full experience of the game. There is a lot good weapons and mechanics I'm not exploring that I might really like if I tried them. Even if I don't like them as much as I like blasting people in the face with the shotgun using different weapons is still a good way to keep the game fresh. Doing the same thing over and over again will make the game feel boring. You might think that the game becoming stale because a player is only using 1 weapon would encourage them to try out other weapons, but is just as likely that players simply conclude that the game is boring.
The gun upgrades in BioShock only compound this preference problem. I can only upgrade 1 weapon at a time and so of course I'm going to upgrade my favorite weapon. If I was over relying on it before it became objectively stronger then it might now be the only weapon I ever use.
Luckily, I can't only use the shotgun. I do have to use other weapons. This is because the number of shotgun shells I can find/buy is limited. While I might want to shoot everyone in the face with the shotgun, I can't. Instead of finding the shotgun shells I want I might find machine gun ammo or pistol rounds.
The number of each type of bullet I can hold is also limited. If I'm fully stocked on machine gun rounds and I find some more, I can't pick them up. BioShock has strong survival elements and resources are scarce. This means that I have to use every weapon at least a little bit otherwise I'm being wasteful in a game that doesn't provide plentiful resources. BioShock doesn't give the player the luxury of leaving ammo behind.
BioShock didn’t invent this ammo system, it is a classic. It is classic because it works so well. The player has to diversify their playstyle yet it still leaves enough room for player preferences to be expressed. The problem is that Plasmids have all the same “preferred weapon” problems that guns do, yet they don't have the ammo system to mitigate those problems.
The limiting system for Plasmid use is basically a mana system. You have X amount of mana (eve) and each ability costs X amount of that mana (eve). All Plasmids share a pool of resources, which because scarcity is such a core part of this game, discourages experimenting with different Plasmids.
Using one Plasmid costs you uses of every other kind of Plasmid. In economics this is called opportunity cost. The cost of an item is how much you paid for it, the opportunity cost of an item is the value of the item you bought (to you) in comparison to everything else you could of bought with that money. By buying one thing you lost the ability to buy other things. Imagine you have 5 dollars and want to buy a snack. You buy a pretzel which is 3 dollars. The cost of the pretzel is the 3 dollars. The opportunity cost of that pretzel is that you don’t get a frozen yogurt (which you might of liked more) because you now don’t have enough money.
When I shoot a pistol in BioShock I’m using up ammo for the pistol. It doesn’t effect my ability to use my beloved shotgun. When I use Incinerate in BioShock I’m giving up a chance to summon a swarm of bees because they draw on the same resource. That is the opportunity cost of that ability. By putting all abilities in direct competition for resources you aren’t encouraging the player to try and use all the abilities, you are encouraging them to save that resource for the “best ability”.
BioShock isn’t alone here, a lot of games with mana systems have this problem. In BioShock it is more noticeable then in most instances because the scarcity in BioShock exaggerates it.
A gun can be objectively worse then all other guns yet still useful because ammo is scare and you have ammo that is only able to be used by that gun. That isn't true for Plasmids because they all share a resource. In order for it to be a good idea to use a Plasmid it doesn't just have to be effective it has to be more effective then every other Plasmid (weighted by the cost of use). This means that using a Plasmid that is slightly worse than a different one is never a good idea.
It is understandable why they opted out of having the same ammo system for Plasmids. For one, they wanted to mechanically differentiate Plasmids and guns. Secondly, it wouldn't make sense from an in game perspective. These powers were supposed to come from within, it is supposed to be your character’s power, and it wouldn't feel like that if you had the same ammo system. I agree that Plasmids should have a different limiting system then guns, I just don't like the one they went with (and then didn't change in the sequels).