Stripe may expand "up market" at some point, but at the moment they're pretty enterprise unfriendly and don't seem interested in becoming enterprise friendly. You can't pay for phone support, their PCI compliance can cause some enterprise customers to blink and even if you're funneling millions through them they won't negotiate on price like other payment gateways. Also many of their more advanced features, just aren't that well implemented or documented (think connected accounts, etc) and since those cases aren't as heavily used we've had to side-channel to a C-level to get an issue expedited after bouncing around support for a show-stopper bug.

Additionally as a sidenote, that market is quite crowded with a LOT of choices. This is certainly not a winner take all industry, there are literally 20+ choices that will be reliable. Typically most large enterprises will end up with a vendor that will give them a good deal on rates, which isn't Stripe.