The reasons we're given for not having a way to see our own DPS in game are really incongruous with what's being requested. If I understand what I'm hearing right, it's something like- "If we give others a way to see their own DPS, then others who can't see that info will somehow make use of this information...." and that's the part that doesn't compute. No matter how you finish that sentence it doesn't matter because people want to see their own numbers in game and that's all their really is to it.
The fact of the matter is, right now people who can't parse DPS numbers (like me, on a PS4) are at a disadvantage to people who can, and that's unfair. Until we have a way to see our own damage numbers in game, players who have the ability can use tools to see their own DPS and our DPS which we ourselves can't see. Most players who are less effective at something than they could be, especially if at a wide margin, would want a way to know that so they can get more output from their time invested. I remember when I was a new level 50 and my rotation was screwed up by a stupid macro I'd been taught to use, and was far less effective without any GCD/off-GCD interweaving. But I didn't really have a way to know that, or even to know how I was doing in relation to others, until I started doing full party instances with my old FC and they were telling me my DPS was really low. There's not a ton you can do with that information when you have no way to gauge where you're at, whether anything you do differently improves things and if so, by how much. And it was frustrating as hell to already be doing the things people were telling you ("You have to make sure you have Straight Shot up, keep two main dot's up if target not almost dead, use Bloodletter procs"- Durrrr really?!?! Cause that's what I was doing.) but you only know you're not hitting a threshold others can see but you can't, you can't experiment with different approaches and know what works best beyond overall impression of how fast things die, and don't know what difference all the stats on the gear you're working for even makes. Luckily someone helped me figure out the problem, and it meant relearning how I timed my instant vs GCD skills, deleting those godawful bard macros that queue GCD skills, maximizing Bloodletter procs, and remapping my controller bar. All for the best but would have been good to know that stuff well before I got to level 50. So I know from firsthand experience there is a lot of frustration and aggravation from people who want to play well and don't have a way to guage and improve their own performance... tryng to solve for that without a DPS meter is like being told "Work smarter, not harder."
I have no idea what my DPS numbers are at now, it's hard to find someone to parse that stuff. During single boss encounters with no adds/dodges to factor in, I'll usually get at least yellow enmity when I'm waiting on quelling strikes to come off cooldown but like others said that doesn't tell me how I'm doing specifically, it's a comparitive gauge that incorporates enmity generation/reduction across the party.
tl;dr Let us see our own DPS numbers please- after all, other people can.