First of all, if you think the worst thing about these jobs is that they're tedious, you really should take a better look at the reports about the working conditions involved.
As for "having it both ways", you're presenting a false dichotomy. You're implying that the society must: either 1) preserve the status quo that makes those people work in those conditions, or 2) eliminate those jobs in a fashion that makes it worse for those people. Those are not the only options.
This is not really a completely new situation that humanity has never faced before. Throughout our history, there have been numerous examples of undesirable jobs being so tightly entangled with the economy that getting rid of them is problematic.
A few examples that come to mind are cocaleros in places like Bolivia, sex tourism for pedophiles in places like Sri Lanka, or child labor just about everywhere. I think that -- despite the horrific lack of empathy present in some other comments -- we can assume most people would agree that these are things we need to get rid of. If you study the history of the efforts to do so, you will find that going about it in a ham-fisted way only makes things worse. Despite that, nobody will argue that the only alternative is to just preserve status quo.