Adding an Australian perspective here. Our politicians did not share the same approach as New Zealand (which started with a level 4 lockdown and stayed there for 6-8 weeks).
The approach here has certainly been more unified than the US, but states are encouraged to pursue their own approaches, with some states (WA, SA, Queensland) having much more success than others (NSW, Victoria). The plan here was never to pursue eradication, but to flatten the curve and keep infection rates manageable.
I wish we'd considered eradication more seriously. As a country we have the resources to support the country through that 6 week period, and the national government would have done a decent enough job in ensuring the population had sufficient support through that period.
Australia's is an interesting case because the recent spike coincides (~2 week lag) with the lifting of most of the restrictions. It's also only really spiking in one state (although NSW may be slipstreaming Victoria).
This is evidence that the lockdown rules were having a significant effect on suppression, and eradication may have been within reach had the easing been delayed another month or two.
But Australia is also an island, in the relevant sense for this discussion, and didn't succeed in eradication.
Hawaii also had considerable success, albeit recently undermined. Much to my chagrin, since I live here.
My conclusion is that eradicating this virus is very difficult, even with all the advantages.
But again, not impossible.