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?
Many modern FPS games are balanced this way for some reason. One thing that bugs me with the modern COD games is that new players start out with poor weapons, while people who are extremely experienced have much better weapons. This means that new players not only suffer from the handicap of being inexperienced, they're also handicapped in the amount of damage they're able to do to other players... This forces new players to be persistent and I guess it makes people value their unlocked items more, than if all items were balanced against each other, and unlocked guns were different
but not better