These are all fair points, but I also think that Nate has had what, a year and a half under Ted, and he still chooses mean. After Rebecca shared her little trick to pump herself up, he decides his thing will be to spit (and we've seen him twice spit in a mirror and not clean it off). Jamie is an example in season 1 of how Ted influenced him to improve (if not in a bit of a round-about way), priming him I think for the self-examination he had to do after he got dumped from Man City and then ask Ted to take him back. Nate consistently skews mean/angry/evil. He didn't take another job, which on some level Ted may have been hurt by but would ultimately have I think supported. He chose to attack Ted, the man who has shown him kindess, support, promoted him, etc., and betray him on a really base level. We've seen Beard try to get through to him twice, once with Roy backing him up.
I don't think Ted can (or should) fix everyone, and I'd like to see him learn that lesson...he needs to keep some kindness and energy for himself in order to heal. Nate is no longer worth his energy.