I'd only want it as a self check to improve myself, definitely. I wouldn't mind one to use for myself.
I like to challenge myself to beat myself out. I honestly don't trust how others would react to anyone's performance information, regardless how well or bad the stats were. It's too easy for targeting a player who may be new, learning an alt, trolled midway (looking at you, feint particle beam mob hustlers and ice orb puddle standers), accidents or etc. I'm usually already beating myself up when I mess up - I don't need people to do the same thing. People who don't want to improve themselves are going to ignore the check regardless who does or doesn't see it. People who do want to improve themselves will. So this is why I really would like having a personal parser - so I can do my own fine tuning while avoiding the trolls.
It would be nice for other players to see the stats and give you advice if they see the DPS/etc being low - but lets face it, the world isn't nice. It would be food for trolls and griefers to go after people - which is just a counterproductive feature to a tool made for being productive. As it is, people aren't always that helpful when someone struggles.
Not really wanting to get into the whole debate about low DPS and kicking and advising and etc - I'm just stating how I feel about the idea of a parser.
I want the parser, but I don't want the grief.
But I do have a possible idea?
How about this - At the end, a window showing lvl/ilvl and your healing/DPS/Defensive scores (based on your job, or not) - and then comparing to the dungeon/trial/raid's average (collected from scores of other random players of similar level - or ilvl if it's level 50 content - that have gone through the dungeon over the past x days) for your role - AND only shown to you, about you. You then have something to compare it to so you can see if you're doing average (and those that don't want to be average can start looking into adjusting their rotation/hunting for info or advice), below average (and again look to better yourself) or above average - in which case, 'good jeorbs'.
I figured 'averages' for dungeons so that it's not directly comparing yourself to the other party members, but rather a % of players - to avoid some of the issues people were stating earlier (player harassment, etc).
Or, if you REALLY wanted comparisons within the party, perhaps bring up the screen AFTER the duty is over (I guess this would only work in DF and not in PF since there would be no anonymity after the run ends in PF) so the people can see the numbers, but not be harassed or do any harassing (or low chance of it). If they want to better themselves, that's still a conscious thought and drive they would have to have regardless if they saw the stats with or without the rest of the party there. People that don't want to just won't, regardless the advice or information given.