Aces are low in cribbage. Their point value is one in pegging and in adding up to 15 during pegging, in the hand, or in the crib. The American Cribbage Congress' Rules of Cribbage define a straight as "a sequence of three or more consecutive cards", and the card order is shown with King as the highest descending normally through Ace as the lowest.
I've never heard of Ace being played high in cribbage, so from my personal experience I don't think it's a common variant, but you could definitely play it that way as an uncommon variant! I don't think it would change the game a great deal.
As far as reasons for Ace being only low, I would use the consistency argument as in your answer. There's no inherent inconsistency in scoring if you think of the order of cards being circular rather than linear, but it does introduce a discontinuity in value. To be consistent, you could play with Aces as in blackjack, taking either 1 or 11, but that would probably make them overpowered, especially in the pegging. And that would introduce more complications, such as would a A 10 4 be counted as one 15 or two? All-in-all, it's more straightforward to stick with the traditional: Ace's value is 1, and it is low.