Except for the fact that, huh, they had siege towers, both at Orgrimmar and Undercity, precisely because they could not just blow them up. The Alliance needed Jaina's magical ship to blow up the decrepit walls of Lordaeron.
It also remains the fact that the Alliance ultimately triumphed at Arathi and Darkshore, the most important battlegrounds in the entire war, while at the same time having enough manpower to siege Orgrimmar, one of the sturdiest military fortress on the planet, AND further managed to hold the line against N'Zoth's armies. So very clearly they did not have such a small army.