This seems odd. The only thing I can think of is that signing NDA's isn't common in the venture scene. The rare times I get push back on NDA's I explain that I had to sign a NDA to get the info and that NDA requires me to manage my sources in accordance with it. Your NDA may also be too broad so you may want to ask if there is a specific issue you can address.

We typically have no problem signing NDAs although I would agree that it's probably overkill from the eye of the lender. For lenders refusing to sign one, see if they can forward an NDA that is compliant per their general counsel. Some lenders won't sign an outside NDA but will have a standard approved NDA that they can sign.

There are a couple reasons why a lender would be hesitant. First and foremost, if it is a large lender, they would need to send it up through compliance/legal to get signed off on. Second, it is a little unusual, and as Ken pointed out, a little overkill from their perspective. Lenders are not only highly regulated, but since they are in the deal community for the long-haul, at the end of the day they succeed or fail by their reputation. That said, I have yet to experience a lender that was a confidentiality problem. Our standard NDA that we have buyers sign includes a provision that allows the buyer to share the confidential information with their CPA and banker.

NDAs are “silly”. They are difficult to enforce. So if you are trying to use someone else’s NDA form, the bank would need to waste time in getting it approved, logging it, quarantining information, reviewing laws for venues, and so on. But here is the crux: banks are reviewing thousands of loan opportunities- NDAs can be tricky (enforceability, liability, joint/severed from employees) because 1) employees and go and do their own thing (independently or work for another business) after being employed by the bank and could drag the original bank into the NDA breach by a rogue employee, 2) will they be precluded from evaluating other deals and could confidential information from one deal be used when evaluating another, and 3) other provisions such as non-solicits can be put into NDAs. A major bank doesn’t want to ever think about hiring limitations from operating level hires from potential clients. It would be burdensome and irrelevant.
If a bank is signing this, they are ignoring it, it will be filed and they don’t give a hoot about it. A bank that refuses is being thoughtful, candid, and honest and saying, “we aren’t signing it, because it is meaningless.” The bank will be reasonable and protect the information because their reputation matters.

I agree that the risk here is low because the bank already has to keep your information confidential. There are a few layers of protection for your business proprietary information. One is contract law, so if you sign an NDA, the counterparty agrees to keep your info confidential and not use it. Second is trade secret law. Trade secret law protects information that provides you an economic advantage but only if you take reasonable precautions to keep confidential. Courts have regularly ruled that the most critical of those reasonable precautions is that you systematically sign NDAs before disclosing that confidential information. If once in a while, confidential information is disclosed without an NDA, the risk is low you lose trade secret protection unless that counterparty makes the info publicly available. Another layer of protection are regulations that require information be kept confidential regardless of whether an NDA signed. As a lawyer, I can't disclose confidential info, NDA or no NDA. There are extensive bank regulations that govern when they can disclose it and it is unlikely a bank would agree to an NDA that contradicts those laws. There is no way to manage different layers of obligations individualized for each applicant.

Almost every bank we spoke to refused to sign any type of NDA, as they claim they're already bound by stricter confidentiality regulations being in banking.

In all reality though, if the only way you can get comfortable sharing confidential information with a certain party is by having them sign an NDA, you shouldn't be sharing information with them in the first place.

NDA's are worth the paper they're printed on.

We will always sign one (but we are required to use our own format), and our Chief Counsel states that an NDA with a bank is not really necessary because we are under confidentiality regulations already,

We always sign an NDA. The only time we would refuse is when the terms are off-market. You should push to get an NDA signed. The banks should have their own templates that legal counsel has vetted that you should perhaps ask to use in order to get comfort on the confidentiality terms.