I think this is a really cool idea that I hope doesn't work out. I agree with others in this thread that is should be based on an open protocol, not bound up in Stripe.
This is my gut reaction and subject to change but...
I say this as someone who uses Stripe heavily and would 100% use them as my "financial provider" (or whatever you'd call the funding source in this system), but owned by them? Ehh, feels way too dangerous to build on top of. I wouldn't trust anyone to be the sole owner of it, I wouldn't want to build my business on top it.
Yes, I build on top of Stripe currently and think they are the best developer experience by far and I've found their costs acceptable for what they've allowed me to build without worrying about the financial side. But, I could switch away from them if they blocked me or I found a better alternative. Making my whole business dependent on them? That's a lot scarier. It's the same reason I didn't use Atlas, even though it would have made things simpler.
It doesn't appear that they own it. More like they're adding infrastructure scaffolding to your project and giving you a CLI to deploy it. From what I can see, nothing breaks if you delete the CLI, and you're fine to deploy it to the same providers on your own or migrate it.