> [...] they cannot control for the willingness to respond to polls at all.

I believe this is not true, because at least ESS (European Social Survey) corrects for non-response, although how exactly is beyond my understanding of survey analysis. Each country reports the response rate as well. See [^1] section 3. Although ESS is much larger survey than simple opinion poll, there are political affiliation questions too (`^prtv.*$` variables).

[^1]: https://www.europeansocialsurvey.org/sites/default/files/202...