I can understand how Regiments are purchased from the points cost of the Hero.

However, other than that is there any other part that a Regiment plays in the game?

It seems that disks can deploy across zones, apart from their Hero and the rest of their Regiment. From a game point of view, each disk is fairly independent after being deployed.

Am I missing something about Regiments or is it just purely for army building purposes?

I think it's just for army-building purposes. Unless I'm in a hurry/don't care, I think about army synergy as a whole rather than building regiments separately.

So far it is only for army-building. Theoretically they could introduce a mechanic that would change this, or give a disk "regimental" abilities, but I doubt that will happen.