I'm more talking about having the information spelled out in-game on the HUD. The depth being removed was more a response to the idea that systems that make the game "too hard" for less aware players should be removed or changed arbitrarily to accommodate those people. An advanced "training" mode would be helpful for some people, but I question whether or not players would make use of such a feature.
"Casual" players probably wouldn't care about anything beyond kill team or capture flag, and they're likely just always going to be "bad", so would theoretically be matched up accordingly. And more competitive-oriented players who want to improve their play can do so the same way they always have: by playing more games, paying closer attention, or analyzing better gameplay. Want to know player/weapon/powerup/vehicle spawn locations and timers without playing more? Go into Forge.
A simple tutorial going through the motions of how to play each gametype along with extra less-obvious things like crouch-jumping and spawn timers would be fine enough, but I also question further whether a tutorial like this is any better than just playing actual matches against like-skilled players, with the contextual pop-ups that already exist in Halo 3 for example. A separate mode being required to learn things that are inherent to successfully completing a particular gametype is a sign of a poorly designed contextual HUD. Something I don't think Halo CE through Reach suffer from whatsoever.
In my opinion, even more advanced things like how to control spawns or time weapons should be left up to individuals, though, as that's part of a strategy, ie: not required to successfully complete the objective of the game. People are aware of it because it happens to them, but why exactly should something like that be relayed in a tutorial mode? You should have to figure out how to better leverage the game's mechanics for yourself based on the information that you can glean from playing or from watching better players.
Something more along the lines of the "
mentor system" in League of Legends (clicky) would be better than a tutorial mode I think. I don't play MOBAs at all, so I don't know anything too specific, but from what I understand, a higher ranked player can choose to be "buddied up" with a lower ranked player as a mentor, to help them improve their strategies. Of course, the lesser skilled player has to choose this mentor as well. Nothing is spelled out by the devs in some "reveal-all" mode, but rather, it is an exchange of information and strategy from one more experienced player to the lesser. Basically an in-game mechanic for how people have always become better at the game. I don't know how exactly this could work in Halo, but a similar "Theatre/Spectator Mode" could be implemented post-game.