I'm in Melbourne, Australia. We have heaps and heaps of cafes here. We are known for our cafe culture. I can actually think of some that fill up, but there are still plenty where you could always reasonably expect a spare seat.
I remember the Starbucks at Shibuya Crossing was mind-blowingly packed.
I think that my argument assumes that you've chosen a cafe with consideration for whether they tend to run out of seats or not.
(Incidentally, I am relocating to Tokyo from Melbourne in a month or twos time. Any tips for me? Any little-known treasures in Japan that I should check out?)