"Useless" is highly subjective when you don't have enough information to render accurate judgment. But this is not the case that we're talking about.
Consider this simplified case. I hire you to sweep the floors in my apartment, and I pay you by the hour. I have a vacuum cleaner, but I don't offer it to you, because then you'd have done the job much sooner, and would be paid less - and I want to pay you more.
Do you see the absurdity in this arrangement? I hope it's fairly obvious. The moral choice in this case is, of course, to let you use the vacuum cleaner, but pay you the same amount as for manual sweeping (minus any amortization costs for the cleaner). I don't lose anything this way, since I've parted with the same amount of money. You have gained, because you've got the same money for less back-breaking work - and now you can either enjoy some extra rest, or perhaps go clean someone else's house and earn more money.
The difference in amount of work you performed in the first case vs the second case is the "useless work" here - and there's nothing subjective about it.
The difference in amount of money paid for a manual sweep and for vacuuming, if you were paid at the same rate for both, is the welfare, because I didn't have to pay you more than the market price of the hour of your work.
Note, I do not consider the term "welfare" to be in any way negative. I just wish we recognized it for what it is, and consciously designed our economic policies around it, instead of pretending that it's something else - in this case, by forcing people to do useless work for it just to satisfy our sense of "propriety" (that they shouldn't "get it for free").