> For larger nations, there simply aren't enough tests available
Why? If your nation is twice as big, then all else equal, your government has twice as much money, twice as many resources, and hence twice as many tests. China now has more tests than they need and they're the 2nd most populous nation in the world.
No amount of money helps if there aren't enough tests available to buy. What is missing are manufacturing and distribution facilities, which of course are calibrated to the normal levels of work and not to a relatively sudden pandemic outbreak of one particular virus.
China has huge resources but has managed so far to keep the infection mostly contained to one specific area. It's not clear how long they'll be able to sustain that or whether they'd have enough resources to go around if all of China were the same as Hubei.
Of course all of this also assumes that tests are effective and that you can then do something useful if you confirm that a patient is indeed infected.
Why? If your nation is twice as big, then all else equal, your government has twice as much money, twice as many resources, and hence twice as many tests. China now has more tests than they need and they're the 2nd most populous nation in the world.