How does direct carrier billing work and who are the biggest vendors?

I am building an SMS service and I have been planning to use Stripe since Stripe is one of the most flexible and easy to use developer platforms in modern history.

However, I think I owe it to myself to try to simplify my service's onboarding to premium plans by investigating direct carrier billing.

Does anyone know who are the large players here? Is it flexible to integrate with them? Does it cost a lot of money for the onboarding, or is it plug and play?

Thanks, I appreciate any answers you can provide!