"Saving bitcoin in banks"? Well, that doesn't sound right, compares to what I know about bitcoin. I haven't seen or heard about any banks that offiacially accept bitcoin in their bank system, so how would you do this when bitcoin is not banks' favour? You can save your bitcoin in all kinds of wallet, you know 
It doesn't sound good because it is against the core values of bitcoin. Bitcoin is a decentralised crypto currency which should remain free from any third party interference. Sender and receiver should be whole and sole authorities to involve in the transaction. I am not against bank or some institutions wishing to provide services against deposited funds but it should not be the main wallet to hold bitcoins
I tend to disagree with your position
In this case (i.e. in the case of Bitcoin banks) there is no third party whatsoever. When you buy things or pay for services with bitcoins, would you consider the seller as a third party? Obviously, not. But it is basically the same with a Bitcoin bank. You don't use it to transfer the money (since you can transfer bitcoin directly), you use the bank as an end-point of sorts. It is not an intermediary. You offer them bitcoins while they offer you percentage on your coins, as simple as it gets. Where is a third party here?
I respect everyone's opinion. The bank would not keep our funds with them (nothing wrong here) as they are supposed to pay interest to the fund depositors.
They will lend our funds to someone else (currently web wallet service providers are not doing this) so my funds will be in the hands of someone else so instead of trusting some single entity (like blockchain.info) I have to trust multiple people (borrowers of banks whom I don't even know). Bank would be third party in this case
As to me, this doesn't change anything in the end
They wouldn't be a third party in respect to you by any definition. Basically, they are one part or side (aka counterparty) in the contract between you, on the one side, and them, on the other. There is no third party in this case (apart from the Bitcoin blockchain itself). It doesn't matter what they do with your bitcoins later (if they do anything at all) and to whom they lend your money (if ever), this is irrelevant and inconsequential to the issue in question. Here's an example to better understand the matter. When you open a deposit account in a regular bank, the bank will obviously be your counterparty in the deposit agreement between you and them (I guess that should go without saying), but government which prints the money which you put in the bank will be a third party in this case since they can devalue the money at any moment (hence comes the idea of a third party risk)
