It's a misconception that there is just one test. There are numerous tests available, some of which are from private companies still awaiting official approval to test humans in the United States.
Testing capacity has also caught up demand in most (though not all) locations, as shown by the testing rate leveling off. This isn't like the early days where tests were so scarce that they were being rationed, although many logistical bottlenecks still remain.
Some institutions are now opting not to test people unless it would alter the response or treatment plan in some way.