Is there any purpose to placing the limited support cards that add 1 power icon (i.e. contested village) into your battlefield, as you can only attack with units?

The only supports that are useful in the Battlefield are ones that protect or enhance the zone they're present in. Ones that just contribute power are pretty much useless.

Yep, well there are ones which rather than affecting the zone affect the unit they are attached to, but essentially you are correct.

Well I figured 'enhance this zone' was a sort of vague reference to that but yeah I should have been clearer.

Perhaps I don't understand this properly, but how are they useless? Doesn't the power they contribute help damage attackers? That may not be much, but I don't think thats worthless.

No, because a support card cannot be designated as a defender so its power is never used in resolving the combat. The only ones which are used in combat are attachments (Organ Gun, Knight Training etc) which add power to their attached unit rather than having their own power.

Ah, thats good to know. I was going to play the game incorrectly!