Eevee represents something that many consider the epitome of pokemon: freedom of choice. Eevee can evolve into one of 7 (now 8) pokemon that we choose depending on how we want to train it. For many trainers, this decision is one of the many reasons eevee is so great. Competitively, it's not such a great pokemon even with Adaptability. But its mythos and what it represents is something so much more. That's where it gets its love from. Personally, I'd never use an eevee in a serious battle, but whenever i find one in a LP, I'm beyond ecstatic.
As far as its evolutions, Flareon is the only one that really is terrible. Leafeon and Glaceon are also pretty bad, but imo they at least have cool sprites. That being said: Sylveon is a monster, Espeon is amazing if it avoids being pursuit trapped, Umbreon and Vaporeon are bulky af, and Jolteon is great when played to its strengths. Aside from Sylveon, the rest of these are ultimately outclassed by others, but in league play or even just in their respective tiers, to overlook them might cost you the game.
Perhaps this is the reason why Game Freak is so slow on creating the full type spectrum of Eeveelutions; because it and a lot of its evolutions are not really all that competitively viable - so why make a whole spectrum?
If that was true, I wouldn't understand from a marketing standpoint - I would buy a plushie of every single one of those bastards.
Bringing up the spectrum, I'm curious what they should do for a normal-type evolution, if they ever make one. I think it was the guidebook of XD that said "if you want a normal type, don't evolve it!" But I don't agree with that; I think it'd be interesting to split the difference and give it a mega.