Very good points, @ke.vernick. To just keep existing accounts open this is a great solution. But if you want to apply for new credit cards you start running into challenges as it’s the mailing address that typically gets reported to the credit bureaus.
So for it to work smoothly for new applications you’ll need to keep the residential address on file for at least one credit card.
But to answer your question about the best CMRAs, I’ve personally been very happy with Virtual Post Mail for the past decade, so I still maintain an account with them in addition to Anytime Mailbox.
But if you can find a cheap and reliable mailbox operator on Anytime Mailbox it’s hard to beat them on price.