Playable Moogles, and why I think it would actually work

[Enkidoh]

In one of the opening cutscenes when starting the game (I think it was the Gridania one) your character sees a moogle and the moogle is surprised that you could see him. Apparently most people can't.

I'm not quite sure how the lore explanation fits that together with the existence of the Moogle Delivery Service. Perhaps whatever explanation is used for that could be extended to player characters. (E.g. Perhaps moogles can choose to be visible or not, but people with the Echo can see them regardless. Then player characters could be moogles who are choosing to be visible to everyone, just as the delivery moogles apparently are.)

It would require a bit of race-specific story exposition to explain them, and currently there isn't much in the game that's race-specific, but I don't think that would be insurmountable.

It was indeed the Gridanian opening which featured the moogles on the carriage (where they invisibly drink the merchant's booze right under his nose!). And when you use the Moogle Delivery Service for the first time, the delivery moogle actually mentions how and why they're being used to run a postal service - the Calamity destroyed the original aetheryte network and linkshells, meaning lines of communication in the immediate aftermath were cut, hence the padjal of Gridania asked them to assist the rebuilding effort by using their abilities of diplomacy and arbitration to help establish a mail service between the citystates (the Beta version specifically mentioned it was actually Kan-E-Senna who was responsible for organizing the moogle mail service, but this was changed in the release version to simply 'the little horned ones' - ala, the padjal in general). In any event, it could kind of be seen as a Gridanian counterpart to how Ul'dah recreated the aetheryte network - Gridania was responsible for setting up the mail system using moogles.

If I remember rightly in version 1.0 there was a quest where a moogle actually revealed they keep themselves out of sight usually because in past time hunters used to actually hunt them to sell as 'exotic animals' to rich Ul'dahns, so now they try to remain hidden for their own protection. Not to mention their language was stated as being generally unintelligible to most people, other than those with the Echo, although this last point has been mostly retconned in ARR. It basically all points to the fact that moogles will never be a playable race in FFXIV.