Why can't the easy fix to Covenant swapping be that once you reach Revered or Exalted with each Covenant that you can go to each hall and speak to the representative and swap out the Covenant. I mean you earned the "respect and trust" through gaining status with them now you should be able to reap the rewards with that you worked towards.
And yes I believe it should be an account achievement, that opens for your alts. Only caveat would be that your initial covenant is where you get the perks, ie mounts, armor xmog, weapon xmog from. You would get the Soulbind Table, Abilities.