Fernplant had a few concerns with this a few years ago, and I'd like to address them accordingly.

1. The other team will be able to call out "Hey Player1, turn around there is a spy behind you." with the advantage of being able to jump to any player and have a 360 camera view around them

Spies will be called out irrespective of a person's mortality. And when a person dies, they are not automatically thinking "Let me click on as many players as I can to find spies in a 3rd person 360 degree camera view." When you are dead, you tend to look at the time left, how many players are alive, what you can relay to the team that will allow for a successful push/defend, openings for big plays and other things. A good spy will do his job regardless of the communication between teammates. In highlander, there is less players (easier to be seen), more communication (harder to execute), yet great spies are extremely effective. Dead talk acts as a TF2 embedded mumble, and teaches players to communicate to help their team win.

2.Warn the team of impeding flanks
Isn't this a good thing? If your team is getting flanked, you should be able to communicate that. This should actually influence your enemies to become better at flanking and maybe correct their timing or routes while they flank.

3.Let your teammates know where the red Spy/Scout is near your spawn that is constantly taking out your teles.
Again, why isn't this a good thing? And sometimes spawn times are really short, maybe less than 10 seconds. After that 10 seconds is up, aren't you going to communicate this information anyway? Is that 10 seconds of dead talk disabled actually THAT beneficial to the spy/scout circling spawn?

Plasma also commented on this. He said, this will cause cluttered comms. If people are cluttering the comms, this would happen regardless of if they are alive or dead. And typically, in hyperion, people don't communicate very much using the MIC. More than half the people are silent, with the rest typing in chat. He stated it might also encourage trolling - Again, the troll will troll regardless of if he is dead or alive. If you don't want people 'spamming' the chat, you can setup a rule for that or auto-gag them if they continue.

He also stated that keeping dead talk off increases skill level. This is actually the complete opposite. Leaving it off decreases skill level all around, because it is easy for the enemy to initiate and harder for the friendly to communicate. If the friendly communicate, it will become harder for the enemy to initiate which will force the enemy to become more tactical, which results in a higher skill cap.

People keep stating that it wouldn't be TF2 if you were allowed to communicate that a spy sapped your building as an engy, or if a spy is at spawn behind everyone. Isn't TF2 a TEAM game? Teams communicate, and if you're worried about your sapper being unsapped due to another engy receiving comms from a person using dead talk, maybe you shouldn't constantly assume that. There are other players on the team that also see things happening in front of them. They MIGHT also comm as well... But even if the result of every comm came from dead talk, so what? Again, if you're the spy circling at spawn, the person will communicate this when he becomes alive. And, as I said before, you'd be forced to become more tactical.

As Mona already stated, TN servers have dead talk on, and it is still relatively simple to succeed in your spy play. Over the years, people have become more and more paranoid of spies,  which forced spies to take a different approach. I think people who are complaining about deadtalk causing spies to be limited should go play in a deadtalk enabled server and come back with their conclusion. I, along with many others, can vouch that the skilled player (spy, scout, etc...) will succeed irrespective of all-talk, dead talk or chat.