Well, another way to look at it is that they fail to stick to their plan because their plan is crap and they don't have what is commonly called an edge here on ET. You can't be 'trading in the zone' if you don't know how the markets work.
That's why I said that psychology is overrated. I didn't say it's insignificant. Far from it. You also need a huge drive to be able to succeed in this business. I'm just saying it shouldn't be the primary focus of someone who's starting out and that in most cases I'd wager to say that their problems aren't psychological, but technical.
Further, the OP asked if I thought it's possible to make money with a true edge, but a 'terrible psychology'.
Of course. You can create a quantitative system and have someone else trade it. Or automate it. Or whatever.
It doesn't work the other way around though since you can't 'trade in the zone' without market knowledge.