Hello,
In fact Training mode = Elo off + no time limit + no penalty whatsoever (leave or time).
"Elo off" option was originally asked by players who wants to play a friendly game here without any "competition spirit", to try things without caring about their rankings. However, it is now also used by players to protect their ELO and not taking any risk.
We wanted to enforce the idea that "Training" is something with absolutely no consequences on anything, with no time pressure, for those who want to test new games or test new strategies (and by the way: "no penalties" implies "no time limit": without penalties time limites do not have any effect). There is no reason to use "Training" for other reasons than discovering new games, test things or playing a game with friends, and for all these things we don't need time limits, penalties and ELO.
I should add that we are preparing a third Game mode dedicated to competitive play. So the Game mode you are looking for if you just want to play without caring about important ratings may be "Normal" in the near future
Hope this helps to understand this design choice.