vay' DaneHbogh yIchargh!
Obviously this idea has problems (makes the missions easier), but some of the survivors have a certain character-- a potential that they never reach during the game, and since the characters don't progress during a "campaign" they never will. Don't you want to see the survivors have all the gear they are "supposed" to have? You wouldn't give them the best versions of those things of course. Maybe for really hard missions.
I can certainly see where you are coming from.
For myself, I feel that starting with weapon (or item) types that are preferred for a given character, could speed up gameplay, which could be useful in certain situations such as demoing a game at a Con or a party.
Overall, however, I like that you never quite know how playing a particular character will go during any given session. At least in terms of equipment.
I also feel that the simplicity of the system and the fact that any character can in fact use any item, added to the redundancy of skill types Barbarian > Iron Rain > Mana Rain, the variations on Bloodlust, Frenzy, and similar, mean that most of the time a Character can do pretty well without having to maximize their potential.
Not saying your idea is without merit for thematic purposes. I personally am just anal enough historically, that in any given RPG I am often going to look for a mini that most closely reflects my vision of a character. So starting with gear that the mini is holding speaks to me in that sense.
I'd say that creating some additional "Starting" cards for particular characters could be useful in one-off situations where demoing the game in a timely manner is more important than playing 100% by the rules.
Though it would also skew the experience somewhat for new players. Maybe create a quest to specifically make use of such theming and playtest it a bunch to see how it could go?
All of this said, if you decide to tinker in some way, let us know how it goes?