Reputation, transparency, and liability would be some thoughts of how to deal with banks without government license and regulation.

Individuals can weigh the risk and benefit of each bank, as they do with custodial bitcoin wallets.

Open source wallets with long track records will be more attractive to users then closed source wallets that where just released yesterday.

Wumbo

agree on the gov't should not tell them who they can do business with.
the license thing is tricky - on one hand, it makes sense, on the other, how do you make sure the process if fair. If we start talking about custodial wallets being banks (which they basically are), then they'd start shutting down one after another because they will not have any licenses. 

kenn_b

bitcoin

The Debanking of Nigel Farage — What Bitcoin Did

I agree on the private business comment but it goes both ways in my opinion.

"Banks are private businesses and they can do as they please" and Government should not be able to tell private business who they can do business with.  Banks should to be able to open with out government license.