Not for lack of trying, to be perfectly honest. The US mitigation response kept the virus just barely under the disaster threshold, despite major figures in the federal government actively opposing most of those measures at one time or another.
But the vaccines worked, so those rich people got it done. mRNA was a gamble, but it paid off with first trials starting just weeks after the virus was sequenced and first doses entering general patients in nine months instead of the 18 we were originally expecting.
But let's not imagine that the US response wasn't otherwise a disaster, especially when compared to places like Australia and Korea who barely needed to wait for the vaccine at all.
So I see people always pointing out SK and NZ and Australia as great examples of handling the virus but it seems to me that naturally controlling travel through an island* would be much easier to do anyway, also an island is unlikely to end up as a major throughfare? Could this factor into the difference at all?
*I know SK isn't technically an island but for all practical purposes it is.
A border policy helps stop infection coming in and internal mask+stay at home policies help when the infection is already in the city. Seoul, Sydney and Melbourne all had big outbreaks. The policies they took were effective in bringing the outbreak within the cities under control.
So yes border control helps but you shouldn't also discount policies such as the 'hard lockdowns' https://www.bbc.com/news/world-australia-53289616 where people cannot leave there homes at all for any reason if there's known cases in the immediate area.
Ok and where is the evidence the spread is significantly due to land border crossings? You really think the U.S. was being infected by Mexicans and Canadians? Refugees? That India is being infected by some or all the countries surrounding them? You must necessarily think these are illegal crossings because legal ones require COVID testing.
All it takes is a critical mass of your own population getting it, followed by wide scale gathering of millions of people with no meaningful mitigations. That's the obvious and simple cause.
How does that square with both Mexico and Canada having significantly milder outbreaks on average? Objectively, aren't we giving it to them and not the reverse?
Taken as a unit with Candada and Mexico, the US is practically an island, it just chooses not to cooperate with its neighbours. There are also islands, which as my own dear sceptred isle, which could have done this and chose not to