Except that it's not a valid reason at all. You're merely feeding on paranoia and stating things that are simply not true. Are there people who would harass others because of parsers? Yes, definitely but people like that are in the minority and, news flash, idiots exist with or without parsers. There hasn't been a single case of people actually proving that parsers actually make player harassment worse. In fact there are various arguments that show that this just isn't the case.
Most good players that I know, and this has been backed up by other players experience, simply do not care about crappy DPS unless they are in a challenging raid. If you're running a simple dungeon like say... Nevereapp then there is no point in stressing over DPS numbers because it's going to be cleared anyway. If you are in an Extreme encounter or Savage then people have every darn right to complain about underperfoming party members because if they can't take criticism then they should not be in raids at all. Not to even mention that there are far more uses for parsers than simply checking DPS read my previous post for a very small summary of this.
I also redirect you to this excellent post.
All you are saying is, "I'm scared someone out there will be mean to me" or blatant exaggerations like, "everyone will suddenly turn into assholes if parsers are available". So your solution? Keep people as ignorant as possible? Screw the PS4 players who can't parse themselves? Parsers will not fix the problems with the community nor will it worsen it but it sure as hell going to offer some very important tools for players to improve themselves, there are plenty of players out there that THINK they are good when they just simply aren't and have no point of reference, which parsers would offer.
Parsers will do way more good for the community than bad by a very large margin and there is not a single justifiable reason we shouldn't have them. I'm also curious as to what you mean by "limited" parsing because that sure doesn’t seem to make much sense.