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Nothing stops you from running it but it's like running ponder instead of Brainstorm. Ponder isn't bad but brainstorm is far better.
Bant gives you consistent turn 1 mana acceleration by playing 4 Hierarch and 4 green sun's zenith. This means you can play a 3 drop with possible daze backup turn 2 almost every game if you want. The best 3 drops in the game are Vendilion Clique and Knight of the Reliquary. Knight of the Reliquary can be a 4/4 turn 2, Elder is a 2/2 shroud turn 2. Big difference.
Personally I like Vendilion Clique best, it's awesome agaist combo, it saves you against decks running Choke (Junk/Rock, GWx Maverick), it gives you valuable information about for instance how safe it is to follow up with a turn 3 Jace The mind Sculptor. etc... It's instant speed (play it end of opponents draw step to kill his hand, or end of opponents turn so he can't bounce it with his own Jace, or before blockers and block instead of dying...)

Then lets talk removal. Only a small portion of the decks out there runs Swords to Plowshares/Path to Exile meaning killing a knight of the Reliquary is often just as hard as killing a creature with shroud.
The decks that do run white are zoo (=faster then Bant), Maverick (is more optimized then bant and runs mother of runes), Bant mirror (Elder vs more Knights/Elspeth/Clique), UWx StoneBlade (plays Wrath of God and Engineered Explosives and a ton of counter).