From a military perspective, I don't see the point of such a massive purchase. You're not excluding any rivals from the area (Western Samoa and Fiji are British and Papua New Guinea is Australian, so there's no point to purchase all of it. There is no historical claim to much of the region.
International waters are large enough that there is no reason to need to purchase all of that territory, as there is no worry about a war against either of the nations in the immediate aftermath. The US doesn't use the archipelago rule, anyway, for delineating naval boundaries. If they did, it might be a different story.
US ships are designed for long distances in mind, and don't need the multitude of bases for coaling/refueling. The sheer surfeit of islands is unnecessary, in that sense.
There's also the issue of convincing Australia to give up some of its territory, much of which Australia fought for in the war. That's incredibly difficult in and of itself.
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Now, not to say that part isn't impossible. Having a potential fallback could be seen as useful, but the best options are either the Solomons or the Bismarck Archipelago. You're going to need an incredibly sweet deal from the US, poor conditions for the UK/Australia/etc. I mean, really really poor conditions, where maintaining the islands is infeasible. That, or incredible defense drawdowns and delegating more to the Empire and the Dominions, which makes Australia feel isolated, and so they give in and sell a nearby port to the US in order to keep the Japanese further away (resulting in a proto-Alliance between the Dominions and the US).
So, you get one more major base in the region, which can act as another fallback potentially. But at most it becomes another Samoa in the long run. It is more likely to be let go as an independent state, but due to its small size, it might keep closer ties (Akin to Micronesia et al in OTL).
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Really to do this, you need a more expansionist and internationalist US.