Why wouldn't you just send the positions to both clients in the same tick? Seems trivial to solve.
"Fixing" this would make movement sluggish: any movement would need to be validated by the server. Meaning delay between pressing keys and actual movement.
So it's sort of a "relativistic" temporal system, not a linear "oh now you're at t=1, now you're at t=2" kind of timeline. And there's all kinds of complicated ways you create concensus between multiple clients, between server and clients, etc. (A lot of this remains an active research area.)
So a server, of course, does send updates (player position, etc.) every "tick," but that doesn't matter. Even assuming zero dropped packets (suppose we're playing over TCP), it would feel like shit (stuttering, rubber-banding, pop-in, jittery physics, etc.) to play a game over a ~60ms latency that updates ~60 times a second vs other people that also are ~60ms from the server, so game engines do a lot of interpolation and servers are in charge of concensus. Hence, it's a bit of a misdirection to say: "can't you just send everyone the right player data every server update?" because servers obviously already do that (and that's not really the hard part, anyway).
Local interpolation and remote concensus is the hard part, and games handle this differently. In CS, for example, two players cannot kill each other (with guns) simultaneously. Valve's engine requires that someone always wins a gunfight (which sometimes can feel random). However, I would argue that feels way better than, e.g. in Halo, where you can headshot each other (and both players die), which feels dumb and frustrating.
So when building these servers, there are lot of tradeoffs to consider (a lot of which might change the feel of the game).
And I explained why this is not feasible given modern network topology. Players move around maps and peek around corners in between these "tick updates" the client gets from the server; therefore, we have to use clever methods of interpolation and prediction as well as server consensus to ensure that gameplay is smooth (e.g. models can't just pop in out of nowhere, movement feels good) while also being as fair as possible (e.g. we don't favor one player's view over another's).
Some games still do this. RTS games notably, but hide it with mouse and sound effects. If anyone remembers the Starcraft 1 option of "extra high latency", it would work by increasing the delay.