While I understand your idea of balancing the game, I don’t think it would be the best decision. Of course nobody wants an overpowered protagonist capable of finishing the game positively no matter what decisions they take, or having a protagonist so weak they can’t beat the game with no matter what they do. However, making EVERYBODY capable of dealing with EVERY situation one way or another is just plain boring and unrealistic.
Most video-games let the player choose the difficult. Since it would be very hard to do this with a game like ZE:SH, wouldn’t the different professions make for an ideal makeshift difficult setting? Some protagonists would have more resources and skills, making them able to deal with several types of situations in several ways, making the game easier. Other protagonists would have limited resources and skills, limiting the situations they could deal with, making the game harder.
If you don’t want to implement the difficult system, at least make the protagonist go through different situations to reach the same outcome. Let’s say, for example, the protagonist needs a sample of the virus to take to a friend who’s making a vaccine. Here’s how they could solve the situation.
For combat-oriented protagonists, they could raid the laboratory by themselves. Inside the laboratory, they would make decisions based on their skills, such as gunning all the zombies down or sneaking through them. They could hack the door, break it open, or use the keycard that requires them to kill all the zombies inside another room and have a high search skill to find. The options are endless.
Anyway, there’s a way for them to survive the situation, but they also need to make decisions based on their skills to solve it. If the protagonist is not combat-oriented, there’s no way for them to get past the lab, no matter their skills. Or at least not without paying dearly for it, be it someone’s live or half their inventory, including important items they’ll miss in some other situations.
Instead, a non-combatant player could leave the task aside until someone else has done it. Let’s suppose that another group took the sample, so they’d need to barter for it. A social-oriented player would have little trouble tricking them into accepting something useless for the sample. A combat-oriented player, on the other hand, would be lucky to trade half their inventory for it.
Of course, they could just get in guns blazing and take it by force. But, if they do take it by force, make them pay, too. They could kill an important character who now won’t show up later in the game to help them, or they could lose a friend in the gunfight. They could also lower said group’s diplomacy to a level so low, that there’s no way they’ll ever be on friendly terms again.
See? Both types of protagonist reached their goals, but by different means. While a con-artist or a MMA fighter could have the highest firearm skills in the whole game, they wouldn’t have the same weaponry as a Soldier or a Cop, making it impossible for them to get past the lab unscratched. Same with the bartering. A Soldier or Cop could have the highest social skills of them all, but they’re so badass and heavily armed that the people with the sample would squeeze them out of everything they have. A con-artist or teenager, on the other hand, would look so weak that they’d take pity and just hand the sample over.
Now, making a teenager survive a trip to a lab with a hundred zombies inside, or making a soldier just burst in guns blazing and kill fifty other armed people at the same time is unrealistic. These situations they just wouldn’t be able to deal with; not satisfactorily at least. Do you want everybody to be able to deal with a situation one way or the other? Fine, but don’t make them able to achieve the best results. Make them go through different situations to achieve the same goal.
It would also give the game a LOT of replay-value. Since each goal would have more than one situation needed to achieve it, players could just play the game over and over taking different routes and never getting tired of playing it.
So, I can think of these two solutions: either make all the players go through the same situations, but deliberately give more attributes and gear to some protagonists, creating a difficulty system, or give the players a multitude of situations to choose from, all of them leading to the same goal, so they can choose whatever fits their protagonist best. Just leave the balance aside.
Oh, and about the bank robber. Well, I didn’t suggest giving them more weapons, just changing the ones they already have. You said they had shotguns and pistols; I only suggested you to trade their pump-action shotguns for Luparas, or specify that their shotguns are pistol-gripped and have manually-shortened barrels.