I think the OP here is talking about a traditional bank that deals mainly in fiat and is friendly towards those who trade cryptos. I see no problem with such a bank. I have no idea how much it would cost to form a bank and I'm not sure how successful it would be since crypto traders are a very small niche to cater towards.
Thank you, yes this is what I meant, a 20th century-type bank founded to promote the interests of the bitcoin community. As long as the big banks keep forcing everyone to stay with them in the 20th century we're stuck with their obsolete financial tools. So we might as well start an old-school bank that will allow bitcoiners to do their business without being harassed and bullied by big corrupt banks.
If you google "how to start a bank" a lot of useful info turns up. According to Huffington post it takes $12 to 20 million to start a bank. Here's what I'm thinking. The community provides the star-up capital through a crowd-funding campaign. We could use one of the alts that have asset exchanges (bitshares, Nxt, counterparty) or we could use kickstarter or something like that. The raised capital will be held by the most trusted escrows in the community (several escrows, this would be too much money to entrust to 1 individual). Then the people running the project apply for the appropriate licences, and if they get approval the bank is open for business. It could be run as a limited liability company, or eventually even as a corporation. Investors would hold assets that could be traded on the exchanges. This way nobody can just run off with the cash. Since it's a legit bank the accounts would be ensured by the government, so even if things don't work out and the bank goes under, account-holders don't loose their fiat.
It's a long-shot, but it would be useful to have a reliable bank for bitcoin trading, at least as long as working with banks is unavoidable for doing business with bitcoin.
As you said, it is rather expensive to start a bank and even if the necessary $10 to 20 million were raised via crowdfunding, there would also be real-world expenses to take into consideration such as rent, salaries, utilities, insurance, etc. Bitcoin traders are a tiny minority in the world today, and established businesses like Coinbase and Bitstamp that deal with Bitcoin already have the paperwork in place and links to mainstream banks. I don't think the profits from bitcoin traders' deposits would be enough to sustain a profitable business.
Your target demographic would be individuals who trade and conduct business with bitcoins. For example, LocalBitcoins traders, altcoin exchanges, shops that accept Bitcoin without using BitPay, etc.