A question: Why aren't we running randomized survey testing to determine the extent of infections?

Who would pay for it? Or do the work, or collate it, or publish the results? Portions of the federal government are actively hostile to fact-based public health work. The rest of it seems to be either defunded or demotivated, as opportunity allows.

Slovakia just tested their whole adult population with antigene tests: https://www.euronews.com/2020/11/03/slovakia-attempts-to-tes...

Yes, it's just a couple milion people & antigen tests are not 100% precize, but it demonstrates something like this can be done.

UK gov is, I was asked to participate (I declined). They even pay you quite a bit of money for the trouble.

Denmark is. Besides very easy and rapid access to free testing for everyone who suspects they might be infected, the government has also sent out requests to random people to get tested.

We are, sort of, when big cities test sewage.

Here in Berlin it's very difficult to get a test, even if you have symptoms. It becomes an issue because even teachers can't get regular tests.

https://allaboutberlin.com/guides/coronavirus#coronavirus-te...