Plausibility Check: American Acquisition of Greenland in 1946

As many of us know, the US attempted to purchase Greenland from Denmark in 1946 for $100 million. The Danes refused, for reasons that, AFAIK, are largely unknown.

Would it be plausible to have a TL where the Americans successfully purchase Greenland from the Danes in the mid-to-late 1940s with a POD not long before that? Would there have to be far-reaching butterflies for this to be plausible? And would simply offering more money have been enough to convince the Danes?
 
The US maintained a base there as it was, and there isn't much besides basing rights to want in Greenland.

So if the US buys it, there will still be a transit base and not much more there.
 
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