Stripe has incredible distribution. For the many merchants already using Stripe, enabling cryptocurrency payments could, depending on its implementation, be as easy as toggling a switch. That's a lot easier and less costly than integrating a new payment processor from scratch. For new merchants, adopting Stripe would mean being able to accept cryptocurrency payments AND benefitting from Stripe's existing product suite and experience. They've solved a lot of difficult problems really well.

Despite the head start other crypto payment processors may have had, imo none have yet been able to produce a developer experience (or even just documentation) anywhere near the quality of Stripe. Also, that "head start" might be a head start in accepting crypto specifically (though Stripe did do this at one point), but it's not a head start when it comes to accepting payments, more generally. I think the things that make Stripe the best payment processor will translate pretty smoothly into making them the best crypto payment processor, too.

I'm not certain that Stripe will become the number one cryptocurrency payment processor, but I think it's likely. I certainly wouldn't put it past them.