Agree for the current US, which is likely a large part of why they have food stamps, but no "living wage for doing whatever suits your fancy".
An argument could be made that much of the government funded research done at Bell Labs is worthless. An argument could be made that of the worthwhile things that have come out of this government research, transistors, lasers, and CCDs are the most far reaching (since transistors begat miniaturized electronics begat cell phones and computers begat the internet).
These government researchers were largely doing "whatever suited their fancy" and most of it was wasted effort and tax money. An argument could be made that the money and effort wasted was worth the amazing results.
The government and by extension its citizens acknowledge and accept that most government funded research won't pan out. Important details that make this work:
1) Only a very small fraction of the population is doing government funded research. Large population supporting small research operations is sustainable.
2) The research is vetted on some level, and it is in a technical field. Technical research has an established history of paying dividends (even though it finds many dead-ends)
I disagree with your point 1): very many Americans are unemployed or underemployed, and being supported by welfare initiatives such as unemployment, medicare, and food stamps. Some significant fraction could be employed doing basic research instead of sitting at home watching TV and looking for jobs that aren't being offered by corporations that are making more profits than ever through fractional reserve lending and bailouts.
An example of underemployment in our industry: there are very many individuals with government funded computer scientists with BS, MS, and PHD degrees, that are employed in lucrative positions as code monkeys and computer janitors. These people should be inventing the next UNIX and IPV8 and advanced networking algorithms and image recognition and self driving cars. I'm not educated on whether strong AI is a pipe dream or not but weak AI has helped with image recognition and encryption breaking and genetic learning and spam filtering and web searching.
I think your initial point that "citizens acknowledge and accept that most government funded research won't pan out" is highly highly controversial in the US among some democrats, republicans, and most libertarians. Many want to cut non-military blue-sky research completely. These people call themselves neo-conservatives, President George W. Bush was a champion of the ethos. Liberals and normal conservatives are a bit sneakier on their wishes to de-fund research.
