Low-skilled dirty jobs should either be automated, or they should be treated like taxation.
Everyone, without exception, has to pitch in and do them - to a reasonable standard, with doubled time for slacking, and serious punishments for avoidance - for [very small number of days a year].
If that sounds authoritarian, consider that's how work already functions for most people - except they're compelled to do it all the time, not just for [very small number of days].