Last spring the US was like "Hey, travel from Italy is all good, let's not worry about it" at the time when severe travel restrictions might have been effective.
I'll grant that people wouldn't put up with them for long, but reasonable measures employed before the infection base gets big can have an enormous impact on the total number of people that get infected.
It's really hard unless you can control borders. Even if the US locked down for 3 months and got to zero, it could be undone by one group of illegal immigrants crossing the border with COVID.
The US and EU were already pretty well infected before they realized what was happening. Only China, S. Korea, and Australia had major outbreaks that were contained, and even those, the outbreaks were fairly isolated (Wuhan, Shincheonji Church, Melbourne).
We've not bothered to do much support for isolation, have high case counts and a year of encouraging people to respond poorly to contact tracing, as if consenting to disease control measures is some unforgivable affront to autonomy.
There are something between 50 000 and 100 000 people each year who are caught trying to illegally cross southern US border. The number of people who are not caught is obviously a multiple of that. This probably could be dealt with, if the government was actually trying to do that.
It won't ever come back at full strength again.
We probably just get yearly shots for different strains at worst.
In the future:
1. Most people will get SARS-CoV-2 antibodies from their mothers
2. Early life exposure will happen
3. The SARS-CoV-2 virus will be force to make expensive mutations to avoid immune escape will come at a cost to fitness.
None of the conditions can be created by what you suggest. You have the problem of having the relatively most-lethal / most-transmissible version of the virus spreading unhindered in a population of >40 year olds who have no natural immunity. The "COVID party" solution maximizes the death and cost of the virus.