Testing randomly gets us a better picture of how widespread it is then testing to confirm severe cases. I'd much rather know that X% of the population has it with an error of Y than Z% of severe cases are due to this virus.

Yes from the research/understanding perspective but a lot of the testing is also to provide healthcare to those most in need. You test the most severe to make sure you can treat them effectively.

100% agree with you, but would also supplement "test the most severe" to be "test the most severe and healthcare workers".

Getting healthcare workers out of quarantine if they aren't infected is also super important.

Both of those come as a priority before surveillance.