Online games work today with fixed ticks and polling usually at half of full frame rate which means that the server updates and polls the client 30 or 60 times a second or any other even multiplier of the expected synced frame rate.
Latency is still absolutely an issue. I play games from Japan with my friends in the states and I often have a ping of 140 ms or so. That is latency, and properly implemented games (Rocket League, for example) will deal with it using UDP among other techniques.
Slower paced games can still use TCP though because latency issues are less sensitive.
You're wrong. Head of line blocking is a real thing that happens very often in TCP.
Edit: parent poster removed that part of the comment between me reading and submitting a reply
Source: I used to write networking stacks for realtime games.
If it's a latency sensitive (like a twitch FPS), UDP is the way to go. Having up to date data is more important than having all the data.
If it's a synchronized game (like a turn based game or an RTS where all clients run at the same logic framerate), or not latency sensitive (an MMO like WOW), TCP is fine and probably easier.