I appreciate the point you are making, so I ask this genuinely: how confident are we in the census count? How confident are we usually, and how did that change given the hurdles the pandemic introduced?
As a census surveyer during the pandemic, I can say that questionnaires are pursued pretty relentlessly, at least in Canada. There will always be some people that refuse or can't be surveyed for some reason, but it's about as accurate as a human to human data collection process can be. The public only has access to somewhat lower resolution data, which probably nullifies the necessity of accounting for every single person anyway.
In some cases, especially with volatile/vulnerable populations living in apartments and what not, we'd revisit the same residence at least 3 times if we don't get it done the first time.
The less than 20% number in some neighborhoods seems like it'd be possible, especially if it's very dangerous, but unlikely, though I don't know the U.S system.
Census data is wildly inaccurate. The percentage of people who fill out the census form is less than 20% in some neighborhoods. Whereas the city knows every time someone flushes a toilet or flips a light switch.
As far as I could find for people who aren’t counted by either census workers or themselves like you mentioned, the Census Bureau tries to get their information through other methods.
This can be proxies, like other people who live in the neighborhood, other government data sets like social security records and postal service data, or through "imputation" which leverages statistical modeling based on the data they do know.
All of the sources I can find suggest that the census is extremely accurate at the large city level, and only obfuscated at lower levels because of the data privacy protections they've put into place.
You do know that if you don't fill out the census form they come knocking on your door, and if you refuse to respond they ask your neighbors and go based on that.
All measurements are estimates, but sometimes the errors look like "we have a machine that spits out 4 all the time" and other times they look like "I saw two people, but I can't rule out the possibility that I spontaneously hallucinated them."
