I seriously think all the Generation 1 Pokemon love is unwarranted. Yes, it started the series, but it ignores just how much of an impact recent generations, particularly Gen 5 and now 6, have had in establishing a new, larger fan-base.
Even when thinking nothing of which generation is represented, Eevee would be a rather clunky character to deal with. Its gimmick is evolving, and we're talking about what is now 8 different eeveelutions. Incorporating each one into a moveset is nightmarish, and as a developer I'd imagine prefering to just work on 8 different characters. And then, even if you incorporate their moves into just Eevee to avoid that, then you're ignoring the point of Eevee, which is to evolve. If it wasn't for that, Eevee would be as relevant as Lillipup.