The Patriot Act and related legislation (notably the Bank Secrecy Act) places regulations on financial institutions operating in the US. These laws require institutions to be able to help the government solve issues related to money laundering or funding of terrorists.
One of the components of these regulations is that institutions must retain records to prove the identities of their customers, i.e. they must implement CIPs, Customer Identity Programs. One of the identifying factors required is proof of a physical address - the regulations prohibit use of PO boxes (other than APO/FPO for armed forces). This is because a PO box makes it easy to obscure your true location - criminals often use PO boxes as a way to hide their identities.
Of course, as you've found, this makes it hard for people who do not have a permanent address.
The good news is, regulations specifically allow you to use alternatives to your own physical home address:
(3) Address, which shall be:
(i) For an individual, a residential or business street address;
(ii) For an individual who does not have a residential or business street address, an Army Post Office (APO) or Fleet Post Office (FPO) box number, or the residential or business street address of next of kin or of another contact individual
So - ultimately - in terms of regulation, you are allowed to use the address for a business, a next of kin, or a "contact individual" - as long as it is a physical street address, and not a PO box.