Things get more complex on the back end of the payment being processed at scale, namely fraud detection and risk mitigation. This is where some of those behemoths in the industry actually shine more.
Stripe passes the risk directly through, you are on your own.
For a lot of folks here working on startups with their first few-hundred customers, that isn't the problem -- the problem is accepting payments and getting back to work. I don't see anyone beating Stripe in that game.
For the folks that have huge customer bases, mitigating risk and dealing with fraud is a much more frequent/costly problem and having a processor help out there is why companies like PayPal (and BrainTree?) are still in people's vocabulary even though a good majority of their experience on the front-end suck.
This is one of those problems that doesn't matter to you at all, until it does... then it is a huge nightmare and you scramble around looking for a solution and suddenly realize why "everyone doesn't just use Stripe" -- or some equally hot new processing startup.