I guess it depends on what counts as handling payments yourself. Stripe can handle just about everything to managing subscriptions and emailing invoices and more. At least nowadays. It’s a lot more advanced than systems that roughly just provide an API to manage payment methods and charge them, like Authorize.net for example.

Also, handling the abstraction between multiple kinds of payment methods (cryptos, different card networks, PayPal, etc.) may also be a considerable amount of complexity that a payment vendor can help with.

I have never directly interacted with the financial system at its lowest levels. I’ve heard it is quite a trip.