I would agree in an absence of historical and military context.

But they

• already had a serious military base outnumbering the Danish troops on the island (since the fifties),
• could invade the island with immense military superiority more or less equally easy with one, three or no bases
• build and use the current base (and by all indications future bases) to cover the Arctic, not to project power against Denmark and the Inuit.

Yes, if this was a Civ game, your logic might apply. But the real situation is more nuanced.

We're installing military bases there, dude.

The US already has a base and dominant military presence on the island. They have been allowed to establish new bases since 1951. Their military presence since WW2 has clearly not been about preparing an invasion.

If the reason to invade was to build more military bases to cover the Arctic, they now have that with no reason to invade.

If there is another reason to invade, the difference between

• a vastly superior military with one base, the permission to build more, and an intention to invade
• a vastly superior military with three bases, the permission to build more, and an intention to invade

is not that great.

Finally, if the point of the bases is to make an invasion easier, the invasion likely won't happen until the bases are finished, giving peace and possibly a regime change in the meantime.

I think you're fucking with me playing dumb.

I'm not. I've followed the US in Greenland with interest for a long time, and read the analyses of the recent deal. I don't think my position is dumb. The US have been flirting with the annexation of Greenland since WW2, and Danish diplomatic counter strategy has always been to allow the US unfettered military access in return for acknowledging that Greenland is part of the Danish kingdom and will remain so. Trump has messed with this relationship, but it is now more or less normalized (for now). This is the best Denmark could've hoped for, realistically.

Would you let foreign war equipment into your country from a country that had threatened to take you by force?

There was already plenty there. And Denmark couldn't defend Greenland if the US invaded, doesn't matter if there is one or three military bases there.

I disagree with your premise that they could have gotten the same results without the threats, therefore this must be benign.

Denmark has been bending backwards for decades to serve as loyal vassals to the US. They joined their illegitimate wars without question. If the US asked for two more bases and whatever else is in the agreement, they would have gotten it.