Aren't there seven Eveelutions, though? Which one would you have to give up?
*starts counting Eveelutions*
Flareon, Jolteon, Vaporeon, Umbreon, Espeon, Leafeon, Glacegon. Yep, 7 Eveelutions. If I had to pick out one as being somewhat less useful than the others, I'd have to go with Flareon, since it has such a limited moveset, but then again if you're going Eveelution-only...
...wait, are you going to be getting them as normal-ability Eveelutions, or are you getting Dream World abilities for them all? Is straight-up Evee available from Dream World with its Dream World ability?
Two are only available post-game; the rest are feasible, if you wish to spend hours catching 6 Eevees at Castelia. =P You could just swap out the Eevee for a flier.
Also, I wish that my base Black City had evolution stones. It had it for a little while, but my Black City reverted to base state after not being played for months. =/ Bad, because I'm starting to evolve all my Pokemon, specifically all the old Pokemon from Kanto and so. xD
Though, that's lucky: I can just migrate from HGSS, if I
really need to. =P