As the US, I look at it as a target of opportunity. If Japan leaves it open, I’ll take it. If not, I’ll bypass it and use Australia.
The thing about the Carolines is that it isnt a whole lot of use to Japan early on, but it is serious pain if the US has it. It allows 1-turn access to many critical locations and that alone makes it worth defending with Japan. But it’s a convenience for the US, not a necessity so it’s not worth taking heavy losses over. I just count it as one more place that Japan has to keep a decent force to discourage the attack which further spreads Japan out.
So in short, the Carolines are not a vital strategic target, but they are a gateway for other critical targets. Take it if you can, but keep in mind that there are other ways to those same targets if it’s too well defended.