I dislike the idea of carriers, it means that the PC death rate is going to be closer to 100% as you cannot keep from trading bodily fluids and a carrier will kill just as well as an actual zombie. To add to that, most carriers are immune to the disease, so eventually, the whole world will be either dead or carriers. The dead will die out (pun intended) because no new zombies are being crated because a zombie attack doesn't create new ones. Death rates will return to something more like normal and cremation will become the rite of passage into the underworld... that or a spike into the brain at death. Like most animals, they will not hunt a diseased member of their own kind, so nothing to draw a zombie anyway.
I've seen it played as a weaker version that is something like a bad flu. You get sick, spend several days violently sick and weak and then recover. It's the same effect as surviving a bite, only more random (Like catching a bad cold).
The problem with any kinda skill set is that you either have to decide if it works, or not. You can run a systemless game with only a few "house rules" that the GM rolls a die and settles the live or die thing. It's incredibly easy with or without a system based game to become a "super" character by simply saying, "I can do everything, see, here's my skill list!" I've seen characters like that and it's more of a drain on a game than a help. If you can do everything what do you need us for? Meat shields while you use your amazing skills? It's hard to create a balanced character without a system, but the problem with a system is that everyone has to have access to it (IE, spend money, have time to read a file, deal with experts who work the system for maximum benefit, etc). Freeform gives more freedom, but GM's have to be careful to make sure that each character isn't too powerful over the rest.
For an example, My won skill set(s) include practical knowledge of most forms of construction, procedural law, research, operation of heavy vehicles, gunsmithing, blacksmithing, fensing and melee combat (formalized compitition, but that's beside the point), camping, chemestry, lock-picking, engine repair, and the list goes on and on. I've had a diverse series of interest and professions over 45 years and I'm a natural student. I also speak a smattering of 4 languages, but really only enough to ask for bathrooms, order food and ask how to get from here to there... also the standard greetings and good byes and the ever important, "How much?" On the down side, I'm blind, in not great health and require some very, very expensive medications that are not common in most pharmacies of the world if I want to survive more than a week.
So, what would I bring to a group in a survival setting? Knowledge and practical, hands-on information and the ability to defend myself at close ranges.... but I would be a burden on the group at large because of the physical.
In short, I would be a fairly balanced character, if I were a character. I've seen characters who could do everything I just listed, and more, who is also exceptionally strong, fit and good looking to boot... what's his downside? "Oh... ummm.. wel.. I get hives from strawberries..." or "I'm afraid of monitor lizards." What a balance!