I see three questions, all sort of separate from each other. The first one seems to be the biggest one,
Is mixing oil paint/acrylic/watercolor inherently different than the
mixing done by screens/printers?
Nope, not different at all, at least for subtractive mixing. Screens use additive mixing (combining wavelength emissions to produce a color), which is a different process. But ultimately, both approaches (additive and subtractive) are controlling the wavelengths that reach the human eye, and therefore controlling the perceived color.
Mixing paints is directly comparable to the mixing done by printers. The main difference? Printers use dedicated computation logic and know their primaries very well, so they can precisely determine how to mix them. Actually, getting paint at a store these days (say, to paint a room in your house/apt) is also done by computer - the store doesn't stock paint of every color, but stocks key primaries (and a white base), and mixes them in front of you to get the color you wanted.
The other questions feel like follow-ups.
This next question seems to be more about economics.
Why not just sell a 3-4 color set and let people mix them?
You're welcome to try, if you think enough people will buy it! Personally, I think an artist interested in mixing their own colors in this way would be better off sourcing their primaries direct from manufacturers, rather than buying a 'set' from someone like me or you, who would have to mark up the price to make a profit.
In the spirit of your questions, you seem to want to know if this could work at all, and if so, the answer is yes (per the first question and answer). An artist doesn't need a whole set of defined colors; they could mix their own from primaries.
Is it feasible to obtain all colors from basic elements?
This depends on what you mean. If by 'all colors' you mean 'all colors humans can perceive', then the answer is 'not feasible'. Using subtractive paints to produce the extremely narrow wavelength a laser can produce is not feasible at all, especially at a high reflectance level so it appears bright. If by 'all colors' you meant 'all reasonable colors that might be included in a paint set', then the answer is yes, again per the answer to the first question.