I shared your hesitation as well, but I don't think Mint is storing your bank password in cleartext anymore at least for Chase. I just signed up for Mint the other day and did not see anything like this for any of my accounts. For Chase, they specifically use Oauth to grant read access to the account.
For me, my checking account is the only banking account I really care about. So much so that I don't use my debit card for purchases and only use it for ATM. I really don't care if my credit card gets stolen since that's their problem and not money out of my pocket.
For me, my checking account is the only banking account I really care about. So much so that I don't use my debit card for purchases and only use it for ATM. I really don't care if my credit card gets stolen since that's their problem and not money out of my pocket.