Sorry i couldn't think of a reason off the top of my head. If there ever was a reason, it would be a personal one between the players, like explaining something that happened in the game or having an irrelevant conversation with a friend that happens to be on the opposite team.
Not ALLOWING players to talk to each other when they are in the same room/server would actually promote segregation, as opposed to dispelling it which is what you are trying to do with eliminating trash talk. Teams would be alienated from each other, and the whole good vs evil mentality would take root. Why do you think every other game, PvP based or otherwise, allows players to talk to each other in-game?

League of Legends, i would assume Dota 2 as well. Really any game that has a respawn timer would have their timer longer than SK, since here its only like 4 seconds. And all those games allow talking across teams.

And if you can still /tell people, what is stopping them from trash talking other players with it then?

If i recall correctly, ever since the sprites update, the timer got significantly reduced.
And LoL/Dota 2 are not the only games, just the first that popped into my head and i've played recently
And not being able to tell anybody besides friends would mean you can't meet anyone new in LD, which usually only occurs when you find a worth opponent (i.e they are on the other team)

All we need is an option to hide the chat box.

There is a constant half-minute timer, be you dead or alive. All peeps have the same synchronized one. Every time that the timer hits the half-minute mark, all dead players respawn. Thus, if you die 1 second after the timer, you wait for 29 seconds. If you die 28 seconds after the timer, you wait for 2 seconds. Ever noticed how your dead team peeps respawn at the same time as you (save for those insta-revive peeps)?

This is a terrible idea, and it actually kind of upsets me because the nature of the OP seems to be the same old political correctness campaign of "A few people said something mean, lets ruin it for everyone!" If someone is trash talking and being rude/offencive/mean, report them and get on with your life? Are you really so insecure with yourself and so unable to control your emotions that you let a few jerks on the internet that are of no consequence to you rule your mind and emotions? Most of the chat I've seen when I play LD is either friendly, playfully aggressive, congratulatory, or all three. When the occasion does arise that I see someone trash talking and/or shaming someone, whether it be towards a (usually superior, and thats why they win, duh) player on the other team or a teammate who isn't that skilled, I may or may not report them based on the nature of their insults, but first I usually try to politely ask them to stop verbally abusing me or whoever it is they are targeting, and that will often times work. Removing chat from lockdown and in between matches would be stupid, it would just make more angry and destructive LD players as well as making those who are already that way even more so, and what would they do then? They would probably migrate to the forums to rant, and nobody wants that.