If you apply the reversal test, the question becomes, in a world where these busywork jobs didn't exist, should we create them?
Or, taking a step back, if you ask "how many busywork jobs should there be?", it would be surprising if the answer is "exactly the number we have right how". So it seems either you should want to eliminate busywork jobs, or create more of them.
To me the "dilemma" smells like status quo bias.
I will say though, status quo bias is not all bad, there is some value to stability, but I'm not convinced it is the role of businesses to provide stability, that seems like a role for government.
It wouldn't be surprising if the dynamics of the human society pushed the number to the current number as being optimally stable for society. Too few busywork jobs and you have large crowds of protesters; to many busyworks jobs and the sectors of the economy that are growing in response to new opportunities are starved of labor. Not really stating a belief but just want to point out that in complex homeostatic systems it there are often dynamics pushing certain numbers to where they indeed are. Certainly true for body temperature and blood pH but no reason in principal not to be true of certain things about economics either.
Society and people's jobs / skills can be shifted rather more easily than bodily systems, though. Just look at the difference in the average day's tasks from 1820 to today.
Provide the right kinds of support, retraining, or yes, UBI, and we're no longer talking about people going hungry when they lose a menial RSI job. We're talking about people whose struggle to make ends meet can change into doing something that feels like a step up in the world.
Having the means to choose your employment is a HUGE thing for a lot of people. Been there, and I can feel the huge weight off my shoulders knowing that if for some reason my current job goes away, that I am certain I can find something comparable.
Should we give our gardeners a lawnmower? Nah that would result in redundancies, leave them with their nail scissors.