You can totally get this kind of flexibility as a self-employed contractor. The fact that you aren't just as easily allowed it as an employee is ultimately due to excess red tape in the paid-employment sector, nothing else. Every bit of red tape in the employment arrangement is an extra fixed cost that has to be paid-for somehow, meaning that the employee has to work that much more just to break even.
Why? There are plenty of concentration effects that go against this; e.g. it's better for everyone to work the same hours for communication reasons.
I've got some news for you, many manual labor jobs aren't just picking up a shovel and digging a hole or picking up a box and setting it back down.
Your first sentence, to me, reads "I'm more valuable than you because I know thing, so I want more resources for less effort".
One can state a fact without making it into a brag. Saying, "I get paid more than you" is not the same as saying, "I am a better person than you", despite the culture that the rich prefer to cultivate that equates the two. A person that gets paid $15/hour is the same amount of person as someone paid $100k/year. The latter is "more valuable" only in the economic, marketplace sense, and gets roughly 3x the resources for the same amount of labor, which likely does not involve work that requires separating ass from chair.
If you don't pay people more to acquire the difficult skills, they won't bother, except in rare cases.
I was only saying the engineer version of myself adds greater resources to an economy than a hypothetical hunter-gatherer version of myself - who, being myself, obviously has equal moral worth.
Congratulations you just described capitalism.
However, I can't truly pick when I want to work. There are no jobs in my area that pay 80% of my current rate for the same task done 4 days a week.
If a job was truly an even exchange of value between employer and employee, I would expect to see some people working 7 days a week and making 40% more than me, and some people working 3 day weeks and making 40% less. But aside from service workers with work on nights, weekends, and holidays, everyone in my city went to work in the dark this morning and will go home in the dark tonight.
I am not against trading labor for money - that's the point of a job. I am against trading freedom plus labor for money.