You normally write very clearly, but I have no idea what you're getting at with this particular comment.
Is any of this sarcasm? Are you sincerely suggesting that not being able to find someone to work for 1 cent per hour means that there is a labor scarcity?
What's this business about public funding of municipal infrastructure and how does it relate to the conversation at hand?
But people's time is always a limited resource. Even in a utopia where the cost of living comfortably is zero and people are immortal, spending an hour providing a service to another person carries an opportunity cost.
So, under this definition there is always, almost tautologically, a scarcity of labor. The word has little meaning, and discussion of whether or not there is such a scarcity becomes irrelevant to decisions about things like public welfare or economic policy.
There is not, tautologically, a desire for labor. I do not desire human computation services at all (remember when "computer" was a job description) or the manual transportation of written information.
You could charge me $0 for these services and I still won't buy any. These are actual jobs that have vanished and there is no scarcity of these services.
You can pretty much automate away specific jobs, like the two you've just mentioned. But there is an infinity of other jobs. And we won't have automated them all away until we arrive at an (impossible?) state of affairs in which there are unlimited, cost-free robots whose physical and intellectual capabilities are on par with humans.
Pick whatever futuristic, heavily-automated world you want to live in: It will still be worth something to you to have someone (for example) spend hours on the web researching a question that you want an answer to (but not badly enough to spend hours yourself).
The irreducible nature of scarcity is pretty much an underpinning of all modern economic theory, right, and taking about it as a variable thing is usually nonsense, and often cover for talking about supply less (or, in the case of discussion of the absence of scarcity, meeting or beyond) one's personal preferences while dressing it up in language that tries to elevate those preferences to objectively privileged standards.
The word has a clear and useful meaning, it's just not appropriate to many of the contexts where it is used specifically to obscure the subjective character of what people are describing when they use the term.
Is any of this sarcasm? Are you sincerely suggesting that not being able to find someone to work for 1 cent per hour means that there is a labor scarcity?
What's this business about public funding of municipal infrastructure and how does it relate to the conversation at hand?