I would say that the kephart, nessmuck, hudson's bay, pukko, and bowie patterns have been "do everything" blade shapes for a long time. Also Japanese tanto and keydashi patterns, I'm sure there are others that I'm not as familiar with.
It would be easier to pick out the specialist knife patterns, such as daggers, skinners (including beaver or muskrat pattern skinners) Flensing knives, weapon retention blades (kabar tdi and similar) or the various fighting knives/bayonets/ smatchet blades.
As a general utility blade, I would say that the oldest would likely be blades with flat "scandi" or chisel grinds, or small near full flat grind blades since for a very long time, steel would not be suited to the uses we put it through today. Blades would have likely been rather delicate compated to today's standards, so a lot had to be done with little, where now we can rely on the strength of modern steels.
The blade with the fewest specializing features would be the most generalist, most "vanilla" blade. It would need to have a very neutral handle shape to allow all grips equally well, a moderate belly, but a ratio of belly to straight blade edge. And a strong, but useable point. So basicly a kephart, with a broomstick handle, and no blade extension below the grip line. Useful, but arguably not ideal for really any work at all. Everything else is some evolution to improve some aspect therein. Be it finger clearance, safety, finer or stronger point. Everything is going to have some cost of another aspect.
As to the idea that people would have access to only one blade I think that is pretty limiting. Consider that while many would own a knife that was primarily for food prep, any trade's person would have a knife or knives that pertain to that trade. A soldier would also have weapons, but the practicalities of life in a mobile camp would have included larger blades for breaking up animal carcasses for food, and axes for firewood. A carpenter would have many which over time go from being axes and drawknives, to bent spoke-haves, and adzes. A farmer would have root knives, hoes, and blades for animal surgery as well as butchery. Consider that some sickle knives are cut to be used with either the right or left hand. That level of specialization would have likely been common when farm tools were either made to order, or made by the user. Even a white collar worker would have had blades suited to his profession, penknives, and other such patterns.
Considering all factors, I think the "for me" do all pattern would be a broad bladed, full flat grind knife with a fairly neutral handle, relatively short blade, and fairly thin.
Given the advantages provided by moderns steels, I'm thinking very much along the lines of the ESEE-3-MH, but with a straighter handle, cpm-3V. Nothing really flash there, but probably not suited to hours of woodwork.