As someone who's been transfering quite a lot of money through various banks and into crypto I'd imaging the biggest issue is the money laundering type regulations. For transfers much over $20k normal banks want documentation where it came from and all your normal transactions can be viewed by the government for tax enforcement purposes. Once you're in crypto that's all out the window - I've been trading on Kucoin which is kind of based in HK or China but no one quite knows where, doesn't keep much in the way of records, if you were transfering crypto out for drugs or tax purposes no one would know. So I can see how Visa would be worried about being party to that kind of thing and then fined or prosecuted for it.

By the way re "no good way in" I've found coinmate.io pretty good once you get the money to them but it has to come from a bank account in your own name and those can be funny about letting you transfer to them. Also it's kind of slow - once your money arrives you have to wait a day or so for a human to process it.