Psychological/Confidence issues aside, I think the majority of his points deficit is actually TOI related.
Points wise:
The problem is largely PP time and total TOI, including offensive starts with the team's best players.
Phoenix and Florida Ballard received, roughly, 2:10 - 2:40 minutes of PP time per game. In Vancouver he (quite rightly, given who is ahead of him) receives none. Ballard without any PP time is a 19-29 point defenceman (82 games), which is absolutely nothing to write home about (actually the 29 ES point season is quite nice, the rest are not).
Why does he only score on a 9-12 point (pro-rated to 82 GP) pace here? I'd be willing to bet it's TOI with the top-2 lines. Florida Ballard received 17:42 of ES ice-time a game for his 29 ES points. Phoenix Ballard received 15:54 of ES ice time for his 19 ES points. Vancouver Ballard receives 14:26 of ice time for his 12 ES points (pro-rated to 82 GP)
That's not a massive difference, but as I said, i'd be willing to bet that the major change has come from seeing time with the top two lines, to seeing time with the bottom two lines. Unfortunately leftwinglock doesn't go back to his Phoenix/Florida days, so I can't confirm that. I think that's more than enough to add the "extra" 12-14 ES points or so he scored in his Florida days (I say 12-14 and not 17 because if you adjust for the ES TOI, that's around what you get). CapGeek shows he was essentially the #3 D-man behind Bouwmeester and McCabe in Florida in 08/09.
If you played Edler exclusively with our 3rd and 4th lines for 14:26 a night, as opposed to our top 2 lines, he would probably be a 10-15 ES point defenceman, rather than a 27 ES point defenceman. And if you further took away his PP time, that's probably around where his points totals would stay.
This is not to say I think Ballard can be an effective top-4 d-man on this team, I don't think he can fulfil a permanent role there. The reason being his outlet pass is pretty average, and it's fairly obvious he prefers to rush the puck up through the neutral zone himself. The problem is this team doesn't play that way and isn't built to play that way. TBH he might be better suited to the eastern conference. If you do put him on a team that is comfortable with this, and give him ~17 minutes ES + 2-3 minutes PP time a night, i'm fairly confident that would be reflected in his points totals returning to the ~30 point level.