Id suggest there are multiple issues at play. First, there are just not enough to go around. Every country on earth is looking to acquire fast and reliable tests. There is a need for hundreds of millions of tests worldwide and they just cannot be produced in large enough quantities at this time. Second, there are multiple types of tests. Easy to use, rapid response testing (think home pregnancy test, but with a finger stick for blood) is easier to use widely, but is generally going to be less accurate than a test that takes 3 days for a result and is run in a lab with precision equipment.
Lastly, if you know the sensitivity and specificity of your test, you can do the math to work backwards from your results to create a range of likely results. While this is not useful to the individual (am I immune or not?) it is still useful when making policy. There is no appreciable difference to knowing exactly 5% of the population has been infected vs a range 3-7% of the population has been infected.
Its all about trade-offs and picking the right test for a given use.