I think testing is poor, but you need to look at deaths per million. USA is still quite low while Italy and Spain are high. USA is 3 per million vs Italy 124. Deaths seem to take awhile so USA could grow.
China's issue was hiding figures and trying to pretend the problem wasn't a real one until it was too late.
China's recovery was to enforce such a total lockdown (at a huge social and economic cost) and having the ability to do so at a 'any price that has to be paid' - and being able to execute on that.
The US's issue seems to be a combination of amazing incompetence (perhaps matched only in specific examples between the Australian Border Force explaining that they don't actually manage the border if it's anything to do with biosecurity, look at the cruise ship issue and now the Sydney airport queueing on international arrival), woeful leadership (federal and state) and as a result the inability of the populace to grasp the nature of what is going on.
All the expert commentary is noting the US is going to have the largest amount of infections, the largest number of deaths and be the largest vector of infection.
That's literally the case here in NSW as far as I can tell from numbers with people travelling back from the US causing more infections than all the people travelling here from China. And yet we shut down travel from China and let people come back from the US..
It feels like I should be saying something like "You cannot make this stuff up.. "