Solicited thoughts on the Training Room . . .
Without a GM, it seems like it's just run your own combat simulations. Which, if one is so inclined, is easier to do alone, rather than with PbP. I suppose it could be useful for learning teamwork between characters. But that implies a foe who needs more than one person to take him down, as opposed to just sparring with each other.
Perhaps, to start, a few simple opponents could be designed, and others could be added as time progressed (inspired or not by existing villains). I could probably find the time to stat up Giant Robot X and a handful of Oddly Themed Villains.
On the subject of damage, I don't think anything should be doing lethal damage in there. If you want to encourage people to use it, then it needs to not penalize them when a mission finally comes up. In PbP, combats can take a long time, and you never know when a new mission will arive. So, all non-real combat for non-real rewards = non-real damage.
I did have one final thought, that it was fairly limited to combat skills. For example, I doubt Handsome could use the Danger Room to practice seducing women . . . or if he could he would never leave the darn thing

But that fermented a different idea in my head, which I presume requires a new proposal . . . so I'll get to work on that.