Mmh, good question... The word "bother" it's a little inappropriate in my opinion: I mean, yes, it's a little "disturbing" (?) sometimes that he's always like... In need of protection, almost like a baby XD But on the other hand I do like the fact that he doesn't like pistolets and violence itself, it's a beautiful side of his character that I personally consider really important to understand what kind of person he is and maybe to understand his feelings in certain situations. So yeah, bothering sometimes but good too :)
It does seems strange that he would be allowed to go out with the agents to potentially dangerous situations and not be issued a gun for self-defense. Still, he doesn't seem 'weak' to me at all, just unarmed and unprepared physically. But toi always get the impression he could use the strength of his wit and intelligence to get out of any situation, which gives him an edge over most people, even the armed ones. :)
I think that Jane could do something if needed. What I mean par that is that he always has a team member with a gun around when he is pulling something where he needs protection. It does bother me though because a lot of times I get scared that he will get hurt and something bad will happed.