I'm more about putting my cards out on display for viewing than locking them up in a deposit box. However, if you collect high dollar cards for investment, perhaps a safe deposit box makes sense. I have a SDB myself, but not for card storage. I'd say the only potential drawback of a SDB is that the gov't can seize your assets that you keep in a SDB if you get into the sort of issues that would warrant such an action.
As for humidty, I don't think you should worry about it unless you're putting your raw cards on display in the bathroom. Even if you did, your cards wouldn't be completely destroyed. As I've mentioned and shared on this forum a few times before, I bought a few T206s that were found nailed to studs behind drywall in a Philadelphia bathroom during a renovation project. My favorite is this dirty Hooker (who was nailed to the stud). It's definitely dirty, but not completely destroyed.