Not OP, but my personal belief is that all work is valuable, otherwise it wouldn't be desired. I don't think it's a good exercise to decide how much it is worth, except to say that work that requires X unit of time should provide at a minimum an amount of compensation that allows a person to obtain a standard of living above the poverty line.
In my book, work has negative utility. It is something you tolerate to get the fruits of it, which may have positive utility. Being paid in exchange for work is the sign that otherwise the work won't be worth doing for you.
The less work you do to achieve a desired result, the better. This is why technical improvements are valuable: they allow you do less work.
There are activities that are rewarding by themselves, like playing games, watching the sunset, or otherwise having leisure. You are not paid for that, you sometimes pay for it yourself, and still it remains worth doing.
I fundamentally disagree with the separation of life into toil and leisure. That mentality debases both acts. It implies that the more miserable our job is, the greater the moral reward we have earned. And, conversely, our leisure must be maximally hedonistic and selfish to make that suffering worthwhile.
All of our waking day is a mixture of good and bad experiences, intertwined with all manner of internal and external rewards and punishments. A hobby is just a job that pays you more in fun than cash, and a job is a weird club you go to more than you want but that pays you dues in return.
Trying to separate them into strict binary options makes it hard to build a complete, balanced life that has all of the various kinds of rewards that are meaningful to you as an individual.
You're describing the utility of work for the worker, and I agree with your description.
But work also has utility for the person who pays the worker, and this is extremely different from what you've described.
This difference in the utility functions for each party (one wants to maximise the return on work and minimize the work; the other wants to minimize the work and the cost on it) is what sets up most of the "classical" marxist class tension. This is despite their agreement that the less paid work that needs to be done, the better.
No, the work done by worker still has a negative utility — it's time spent and salary paid, a clear loss for the employer.
The fruit of the work done is what's valuable, thus is what the employer buys from the worker by paying wages, or a slave owner forcibly takes from a slave. This is why an employer is interested in technical improvements: they reduce the required amount of work per unit of the resulting valuables.
The tension between the worker and the employer is about the price paid for the fruits of the work. Definitely, with standardized industrial manufacturing, it's about the amount of time and work conditions, because a worker can't significantly influence the performance of the machines he's using, or could not at Marx's times. As the Japanese (e.g. Toyota) have shown, workers with right motivation and right education can influence performance of industrial manufacturing quite significantly, e.g. by spotting inefficiencies and by lowering the defect rate.
The way you are doing the accounting here, it's like the supplies used in manufacturing have negative utility -- they are a cost paid, "a clear loss for the manufacturer".
Work has positive utility when it creates something of value. Considering the money paid for it as coextensive with the work is a mistake because people can work to create value without getting paid, as sometimes happens to unfortunate people. It is no more reasonable to treat the work inputs into a good as having negative utility as it is to treat the money paid for it as having negative value.
I'm not making a distinction of how valuable a particular piece of work is, just that work in general is valuable and should be valued such that whoever is employed by it should be able to be sustained by it.
If a person desires work but doesn't value it high enough to sustain a person whose time is wholly consumed by it, I would question the necessity of that piece of work. If it's not critical to your business maybe it shouldn't be done. If it is critical then it sounds like it's worth the compensation.
Sometimes someone's valuation of work is questionable. It may have had value to them, i.e. they paid someone to waste time out of pity, or their valuation could be wrong. They could pay someone to pray their stock prices increase not realizing it's useless.
There are much more obscure ways in which work can be entirely useless without anyone noticing, and plenty of ways people can end up with jobs that are pretty obviously a waste of time.
