You are right in that games have latency inherent to the processing of game engine ticks and depending on when you press the button the server might have just advanced to the next frame when your input gets processed and you're looking at another delay of potentially tens of milliseconds on top of network round trip and of course however long it takes the game to draw the updated info on your screen once the information gets back.

Wonder if it would make sense nowadays to send world state updates to clients at 1000 Hz or if it's even feasible?

A lot of people play with 144hz (what I play on) and some even higher (240hz). Which is just under 7ms and just over 4ms, respectively.

He's talking about network frames, not graphics frames.