Pretty much what Frejya said.
I can see parse numbers to be demanded to be told when a DPS check fails. Any negative behavior that would happen with the group parser would happen then too.
Conversely, the benefit of a group parser is someone can compare their DPS to others in neutral settings (i.e. Expert Roulette). Maybe you've been fairly happy with your damage output all along, and then get partnered up with someone else of the same job. Looks like you have better gear, you should own them right!? Wait, your DPS is only half of what they have. What?? That can't be?! OK, time to accept it and figure out what they're doing that you can emulate to improve.
With the personal parser only, this would never happen and the only time comparative data would come would be in the negative situations. Many positive comparisons would be lost.
AND if you had a personal parser only and did the ex roulette, if afterward you asked what the other DPS was doing - you'd inadvertently sound like an elitist. Even though all you want is to compare your numbers to see how you're doing.