While it may be very objective, I think some kind of baseball type error system would work better. If some idiot decides to go for a bad linechange, that results in an odd man rush, dock him. If a defender coughs up the puck that directly results in a goal against, dock him. If a goalie lets in a ridiculously soft goal that any peewee goalie should have been able to stop, dock him.
The baseball-type error system is even worse than the current +\- system, since it makes it more 'subjective' rather than 'objective'.
The fatal flaw with the current baseball-type error system and what would carry over to your proposed system, is that it will not take 'range' into considersation.
What do I mean? Let's take your example. The defender who coughs up the puck will be docked a point, however, he's involved in the play. The player who is not involved in the play will not be docked a point. Therefore, the uninvolved player will be judged as defensively superior.
It happens all the time. Some players in baseball have the ball hit to them over 100 times less than other players at the same position, which decreases their chances of making an 'error'. You want the players to be more involved in the play, and possess more 'range' -- even if they make more mistakes. A player that gets to a ball and makes an error showcases more defensive-ability than a player who does not get to the ball at all.
The baseball-type error system under an NHL format would continue to suffer from this ignorance.
That's very objective, too. There are some good penalties to take, and there are dumb ones.
You want more objective. Even if +\- is a bad stat, it is still completely objective.
Not really.
If you're on the ice when your team score a goal, plus.
If you're on the ice when your team is scored against, minus.
What is so useless about tracking the ins and outs?
While it's great to look at results, as that is all that matters, it is irrelevant when the results are tainted. In this case, with +\-, the results are exactly that: tainted.
The stat suffers the same fate as many other hockey stats: it is largely team-driven, so it is hard to quantify a player's contributions both offensively and defensively without considering a proponent's teammates.