This is a "feature" inherited from the original. Given that terror sites always appear in the dark of the night, I think that there should be some strategical option to be able to tackle the battle under some of your terms too. I agree that if you have enough bases and crafts you could theoretically keep a terror open forever, bu I think this is best left as-is.
Edit: there have been talks (can't find the post now) to have some penalty involved when taking too long to reach a battle site (not only terror sites), like having a limited number of turns until the aliens fix their ship and leave, or find that some of the civilians have already been killed, etc.