That's a very strong assertion that needs proof. Testing is important, but so are many other things like access to hospital beds, ventilators, face masks, etc.
Plus you are assuming that states would have been uniformly aggressive in testing and countermeasures, which is manifestly not the case. (See Louisiana, Florida, and NYC for examples.)
The proof is self-evident. There are a plethora of commercial labs that were not allowed to do testing, and the CDC's one blessed test was a failure. Had they not been the sole blessed entity allowed to do testing, states could've run things better on their own.
Better testing could've contained it long enough to allow us to prepare for the mitigation phase we're thrown into, unprepared again.
As for the states, not every state would've done well, but it's practically impossible for it to be handled worse than the way it was. The US response has been a disaster from the top down.
If you are going to run 'what if' scenarios it's worth asking what if somebody like Mario Cuomo had been in the White House in early January? (Or any of several other US governors for that matter.)
I have been thinking all along that even someone who has been dead for five years would be a suitable replacement for current leadership.
Seriously though, yes, Andrew Cuomo is a walking demonstration of what competent leadership looks like. I wish we had that at the federal level.
https://www.factcheck.org/2020/03/trumps-misplaced-blame-on-...
There was no rule anyone has found that restricted other labs from testing.