The reason Gnomes can be Warriors is because it's not exactly rocket science to learn how to fight with weapons.
The reason Night Elves can be Mages is because a formerly secretive sect of Night Elves who still practiced Arcane magic has rejoined the main Night Elf society due to the Cataclysm. Prior to this, Night Elves detested Arcane magic due to it causing the world to be invaded by demons, which was narrowly defeated.
Blood Elf Druids don't work because Blood Elves' ancestors were Night Elves who couldn't bare to give up Arcane magic and were exiled to where they live now. They set up a big fountain of magical power (The Sunwell), called themselves High Elves and went about there magicy business.
Then Warcraft 3 pops along and Arthas utterly corrupts the Sunwell to raise his BFF Kel'Thuzad as a Lich. High Elves lose source of magical power and realise they were quite addicted to that stuff, survivors of Arthas' attck rename themselves the Blood Elves. At the end of The Burning Crusade, the Sunwell is restore as a fountain of Light, not Arcane magic.
Addiction to Arcane magic lies at the heart of most Blood Elves. Nature magic is beyond them because of this, so Blood Elf Druids just aren't possible for the forseeable future.