There's a whole spectrum from instant re-spawn to permadeath.

Side-note: in COD it depends on the game mode, and instant-respawn modes stem from the early FPS games where it was standard.

In my recollection, Counter-Strike popularized the 1-life-per-round team vs team type system within FPS games. It existed in others before that, but CS very suddenly became the most popular online FPS, making it a common standard.

In the CS system, dying can result in up to a 5 minute wait, while you're left to spectate the rest of the battle. This puts a much larger emphasis on playing carefully rather than running around like a headless chicken.

CS (or some COD modes) is also focussed on a match of skill between two teams trying to complete/prevent an objective. It's supposed to be (somewhat) tactical game with tension building as the player count on each team dwindles. If a team that's down to 2 players comes back to win against a team that still has 5 players, it's exciting. The limited lives per round is a source of drama, as well as a behavioural modifier.

If it had instant re-spawn, it would be a completely different kind of game, so this is like asking why every game doesn't have vehicles and rocket launchers and jetpacks!

Being frustrated by dying in that kind of game is by design. You're supposed to regret and reflect upon the choices that led to your death, and you're given the opportunity to spectate the fate of your team-mates. This in turn affects the behaviour of the players, so a COD player in a deathmatch mode will behave differently to a COD player in a one-life team mode.

If you can't deal with idle reflection for 10 seconds to a few minutes, then don't play that kind of game.

Seriously, I do not understand at all when I play COD and see people raging about a 10s re-spawn timer. I just assume these people must have ADHD

In a quake/deathmatch game on the other hand, the idea is to constantly be as active as possible, being on the move and always attacking, in order to get your kills count up as high as possible as quickly as possible. Time you spent dead is time that other players are increasing their score, while you're not, so you want to respawn as fast as possible and get back to it.

Increasing the respawn timer here acts as a penalty for losing a battle, which leads to a score feedback loop -- winners don't die, so have more game time per match, which gives them more opportunity to gain points / losers are penalized with less time per match, which gives them less ability to gain points. These kinds of feedback loops create more contrast between different skill levels on the scoreboard.

At the other extreme, in a perma-death game, you might play a character for hours (or days, weeks, months) and when that character dies, they don't come back. This is a completely different kind of fun, and results in completely different kinds of behaviours. Players in this game are not going to act like Quake/COD players -- they're not going to run around in the open, guns blazing, hoping they'll head-shot, their enemies before they get shot themselves. They'll slowly crawl from cover to cover, using binoculars to see if anyone is hiding in distant windows, spend minutes scouting areas to ensure it's safe before revealing themselves, etc... and when combat occurs, they may even feel real fear due to the real possibility of losing something. They may even empathise (that's not a word you associate with COD/CS/Quake) when they kill someone, knowing they've just erased days of work! That ability to evoke real empathy and emotion is not something that a meaningless deathmatch game is capable of (in my experience), so they're each a different kind of art, made for different purposes, aimed at different demographics.

You can push it to the extreme in the other direction --

In games like Battlefield or TF2, you respawn at some kind of "start" area.

what if instead of re-spawning back at the start of the level, you respawned where you were 10 seconds ago... or what if you re-spawned in the very spot that you died after a 5 second delay?

What if you re-spawned where you died without any delay?

That's pushing it to the extreme where it becomes stupid -- at that point, there is no dying any more

With the others though, dying would be much less impactful. If there's 60 people in a big firefight, then after half of them have all shot each other to death, there will still be 60 people in the firefight, because the dead people would've popped back up again.

This is actually relevant in the Battlefield games where you can spawn on your squad leader's position. Without a respawn timer, there would be no death (except for the squad leader)!

In games with "starting zones", then having a 10s respawn timer is the same as simply moving the respawn zone 10 seconds worth of running further away. Both affect the amount of time it takes for reinforcements to get to a battle.

In TF2, you're usually trying to kill people in order to clear a path for your team to reach an objective. It's about "map control". When you kill everyone in an area, your team can move up to that area and occupy it, in order to start trying to clear the next battle zone.

As you push towards the enemy "starting zone", the time it takes their reinforcements to arrive gets less and less (travel time from spawn zone to battle decreases), which increases their defender's advantage. A spawn timer here acts as a minimum reinforcement time, making it actually possible to push a team back all the way to their own base.

With instant respawns, and spawn zones that are close to objectives, the objectives would be impossible. A spawn timer lets the map designer place the defenders' spawn zone close to the objective for convenience, while maintaining the balance that would normally be achieved by having the defenders spawn further away.

For a pure free-for-all deathmatch game, then either placing spawn points far away from typical battle areas and/or using a respawn timer is a way to dictate the pacing of the game.

Again, we can take it to the extreme: imagine the level is just one small room that everyone respawns in without delay; the game would be completely chaotic.

The designers might have found through experiment that it was simply not fun to be constantly fighting and respawning instantly back into fights again. It might be too taxing on the player, or it might de-emphasise the skill of fighting in favour of random button mashing, etc, as there is barely any consequence of dying...

They might have found that giving players 10 seconds of "down time" between fights results in a more dramatic experience.

What kind of respawn timers are we talking about anyway?

IMHO, anything under 3 seconds is pretty much "instant", and 3-10 seconds isn't really noticeable (hence my confusion when people ragequit a server because of 10s spawn timers). 20 seconds - 2 minutes is long, but ok if there's a good spectator mode and there's something dramatic to spectate. Longer than that and I'd get impatient.

but doesn't it sacrifice gameplay enjoyment especialy for newer players who will be die far more that experienced better players?