Small banks would probably appreciate the open-source software since they would lack the resources and expertise to develop their own. Large banks could develop their own custom software if they like.
Oh I think they should rather be scared than appreciate. This is others' people money business and they need to have everything as secure as possible. If they don't understand something (because of lack of resources), they won't try to take shortcuts. You have no guaranties with open source software, heck, you are even aware that it was created and is maintained by someone who is not paid to do so. You don't know how secure it is. You don't know how long it will be maintained and if it won't be abandoned next month. Until the software is mature enough and mainstream enough (think Linux, Apache, etc - this is a pretty small club), you just don't make millions of your customers money depend on it.
Cold storage is useful and secure, but it just refers to offline storage of coins. That's the equivalent of putting your money in a secure vault at home, I think. While I'm sure this is quite useful, it addresses a somewhat different problem than banking.
In bitcoin world, I don't need banks to conduct transactions. In real world when you want to send money to someone, you need an intermediary - wether it will be a bank, a Western Union or a postal service where you put cash into an envelope. I don't need a bank for bitcoin transfer. While that off-blockchain ledger might help bitcoin system in overall, it won't help me personally so I have no reason to use banks to transfer my bitcoins and no one will have. Their transaction volume will come from people storing coins with them in the first place and then sending them.
(well, there might be a reason to use off-ledger transfers on day, which is payments; I can imagine number of transactions being so high one day, that you'd need to include 1 BTC fee to be sure that the miners take your transaction within the next few blocks; off-ledger, bank-processed transfers might actually become cheaper one day when it comes to small to mid value transactions)
So I think for now there's storing and securing my coins what's left in terms of reasons why I might want to use a bank instead of taking care of myself. They would need to provide more secure and/or more convenient way to store and use bitcoins for their services to be desired. And that's why I thought about them about secure storage facilities in the first place.
I think that this would be the biggest reason of bitcoin banks existence - secure storage and convenient usage (and easier exchange, but banks wouldn't like to jump into bitcoins to limit themselves to be only money changers). The average Joe is not able to properly secure his bitcoins. Even members of this forum are regularly hacked out of their bitcoins, and they are well above average tech savviness. This is where banks can step up and show people the secure and convenient way of owning and using bitcoins. Also taking responsibility for technical failures. Which leads us to:
I hadn't thought about the insurance problem. Although of course, none of your bitcoins are insured now, so that is not really a step backward from the present situation.
It is a step backwards if you can properly secure your coins on your own. If there will be a “Hello, we are Bitcoin Xtra Secure Vault Limited, Belize registered, and we just created a bitcoin bank so that you can safely store your bitcoins, we encourage your deposits” bank which came out of the blue, I wouldn't trust them with my savings and I'd prefer my uninsured cold storages over their uninsured not-really-sure-what. As far as I know that bank might be a 3-person operation with more boldness than experience or knowledge.
Now, when it comes to real-world banks, especially the bigger ones, I could trust their IT, their being insured, their being big enough so that an average-sized theft won't have an impact and will be refunded, etc. They are already handling so much money that they know how to do it properly and if they decide to implement a new protocol, I believe they do it right. Until that happens, I am handling my bitcoins on my own.
There is a long road before that might happen, but I believe it's viable in ten years perspective. You might have your BTC, LTC, etc, accounts just next to your USD accounts and they all would use the same banking interface, so you really won't feel much difference. Except knowing that there are no chargebacks for sent coins.