If you have recurring payments, moving the payment methods over is a non-trivial amount of time and coordination to get done (and I'm not even sure how cooperative Stripe will be if you're on a fraud radar somewhere), and usually only involves the raw methods themselves, stuff like subscriptions you'll need to rebuild.

I don't think it's a bad idea necessarily, but it's very difficult to almost impossible to make this a "flip the switch" setup, particularly for SaaS businesses which are almost always recurring payments.

We're a largish Connect user and for us the key thing is just establishing good relationships with reps in the company and maintaining those. We've had a couple of customers run into freezes and other issues and while standard support is basically a brick wall in those cases, getting someone internal to escalate can be hugely beneficial.