Don't know if it is defined as a character issue but not sure about this given the situation he was in at the time
https://nypost.com/2017/11/03/rangers-benched-defenseman-ive-been-playing-pretty-well/
I'm speculating but maybe that was the start and he just never relented to thinking maybe he was not playing pretty well. At some point what does a team do when scratches and whatnot is not changing the player's opinion of their game?
All in all is was a poorly thought out trade given the bad outcomes outnumbered the good outcomes.
1) He played well and earned his next pure UFA deal and was able to play up to it.
2) He played poorly and the Rangers traded what they did (a 2nd and 3rd) for that and they let him walk.
3) He played okay and they needed to re-sign him as a UFA or let him walk giving up what they traded to get him in the first place.
4) He played well, then regressed after getting a new contract.
Since he was having some difficulty consistently playing up to his last contract I'm not sure the Rangers really calculated the risk reward within the possible outcomes correctly.
Most of that does not just go for Smith, those are the possible outcomes when renting any pending free agent player at a deadline, the same outcomes applied to E Staal, Clowe, etc.
Even if not a pending UFA, Rangers imported some pending RFAs at this deadline, carries less risk as the player can not just clean walk away as a free agent but perhaps using some caution to not to base any offers on a small sample sized honeymoon period would be prudent.