Personally, it would be interesting for Eevee to be a starter, but your rival would have to have Eevee as a starter too. Why?
Well, as in any Pokemon game, your rival always has a Pokemon strong against yours. So if you were to have Eevee as a starter, they'd have to start with Eevee too, and they would evolve it into an Eeveelution that has an advantage over yours. The only problem with this, however, is if you choose to evolve Eevee into Umbreon or Jolteon, but I suppose your rival could find a way to make his Eeveelution strong against either, e.g. evolving it into Leafeon to counter Jolteon (electric moves don't do much against Grass types).
But yeah. The Pokemon producers probably want to keep the grass/fire/water starters, but who knows? Maybe Eevee will be a starter one day :/