Say what you want about the mans' personal life, but Matt was a solid wrestler and was actually a much better wrestler than his high-flying brother Jeff, even if his accomplishments might not show it.
Aside from that, Matt Hardy brings a lot of tag-team experience to the table, and in a time when WWE is having difficulty with that part of it's programming, I think that's a good trait to have.
On a more personal note, I think Hardy is also well aware of the pitfalls that can come through the life of a professional wrestler, and I think he'd be a good person to have on staff to catch people who may be having problems and pull them out of any potentially hazardous situations like the one former NXT/FCW Diva Buggy Nova went through.
I'm sure a lot of people would be perplexed at why Helms would be so valued a trainer, but I think Helms did something not a lot of people did and did it surprisingly well. What I'm referring to was his ability to seamlessly go from fun-loving superhero Hurricane to the jerk that was Gregory Helms' "true" persona, and he found success at both roles.
Not everyone needs this ability, but I think for a guy like Richie Steamboat, for example, Helms' aid could be beneficial to him in the future.
Add to that, Helms is a skilled wrestler.
You know, it's a shame. For all the good things Nash could actually do it seems people can't seem to get over the fact that Nash has bad quadriceps and held down other stars to hold on to his spot. It's not his fault he worked in a broken system that rewarded the tall...you know, I'm not even going to get into that right now.
The reason I think Nash would be a good trainer in NXT is because he can do something most big men can't do, and that's talk. Say what you want, but the man has charisma and the man has mic skills. Something most big men (Jack Swagger, Brock Lesnar, etc) seem to lack. I think getting the chance to work with Nash on that skill could be helpful for these bigger superstars.
Aside from that, I think Nash has quite the mind for the business, which is something he can help to pass along to the other superstars as well.
Adam "Edge" Copeland
This is the man who, if it was up to me, would be the head trainer of NXT. Edge was one of the few total-package superstars. He could wrestle, he could talk, he could adapt—simply put, Edge was a talented man.
With all the people Edge has seen come and go, and with his own ability, I have to think Edge would be a good judge as far as seeing who has what it takes to be a WWE Superstar. Having had the chance to work with some of the best in the business from Hulk Hogan to HBK to Cena to Orton to Punk to Mysterio to Undertaker, I can't think of a trait Edge couldn't pick up on in a superstar and help them to exploit, and of course, this would allow Edge a good job without him having to do much traveling.