I trust TF (this is key to using Inputs, IMO),
Sure, but do you trust any and all government agencies not to shut him down?
Do you trust him not to ever die, or to have made appropriate arrangements for you to continue to access your bitcoins if he does die?
Do you trust everyone that he has given access to the service (including those who have access after his death)?
No, but I should clarify, if I didn't, that I don't feel secure (period) using an online wallet. It is only for temporary / short-term use or small BTC balances. You bring up good points.