From a game design point of view, if the game has DPS and HPS challenges, the player should be provided the tools to measure their performance against those checks in my opinion.

A parser doesn't really help your performance, especially if you already play well, but it provides a wealth of information. Making use of that knowledge is a different matter altogether. A simple DPS number is not all that useful, especially for a casual player, except for maybe making them realize their actual performance level. It might spark them to research their gameplay but simply knowing your DPS compared to others doesn't do much for them. It won't turn a wipe into a clear for example. The important part, however, is knowing why the wipe happened, and this knowledge is something an in-depth parser can provide. Skills used, actions per minute, buffs and debuffs, damage taken: these are the important things, not the final DPS number.

"What is my DPS?" is not the right question nor an interesting one. "Why is my DPS the way it is?" is the thing everyone should be asking themselves.