Anything Stripe builds is going to be orders of magnitude more battle-tested and reliable than anything I could possibly build. This is such a mission critical piece of an application, _I don't want to avoid touching it as much as possible_.
Now it will take a couple lines of code to add another unit to a customer's monthly bill instead of dozens of lines of code and an extra database table. It's not too complicated, but it's enough to make it much likelier that I'd introduce a stupid bug.
For me, that's the benefit.
Context -- I'm a young programmer and don't trust my own code as a matter of course, and I'm working in a bootstrapped-to-the-hilt startup where any ounce of effort saved is gold.