There are not many 'balanced' battlegroups, let alone Alliance dominated ones since faction changes. Horde dominate many BGs only on "pure numbers" alone, considering the many imba starts in BGs favor of the Horde.
Since the majority of PVP focused people, as well as those 'lazy/bad' ones wanting to be
'carried' faction transferred to Horde, Queue times on Horde on most battlegroups had increased considerably.
They tried 'enforcing' equal starts in BGs, but due to the massive horde crying about long queue times, it was reverted.
WG Balance to some extent also came into play on some servers. The vast majority of PVP servers are horde dominated in numbers, so they control WG 90%+ of the time.
When it's easier as Alliance to move to a PVE server and farm honor faster in heroics than losing every BG, it goes to show the 'lack' of interest in PVP as Alliance.
Faction Changes started the decline of the Alliance PVP population, x-realm heroics killed off whats left of the minority/underdog Alliance PVP population.