My wife sells knitting related things (patterns, books, yarn) on ravelry.com. They collect the payment for her and transfer the money to her paypal account. I suspect it will be a while before stripe can do such a thing.
From there, your wife could transfer the money directly into her own regular bank account.
If ravelry.com goes out of business before they transfer the money to her paypal account, there is no chance that they can take any of her money with them. (While highly illegal, I've seen this happen elsewhere with a similar setup.)
We are fortunate enough (being new and in closed beta) in that our audience knows who we are and that we're not a random sketch site. Down the road, we probably will have to support PayPal again (though very differently), but for now our current state (closed beta) and our business model allow Stripe and traditional payment gateway-only checkout.
With that said, I will put a huge "YMMV" here! This is obviously not OK for every site, and the privacy concerns are very valid.
Our current enrollment process is so fast and simple with Stripe that we're curious to see if our conversion rate is -better-, for our current audience (older, non-technical users at this point). While a $30-$90 course isn't an impulse buy, lowering the barrier to enrolling in more than one may leave us better off.
But we'll be able to discuss that better after we have more data.