title_body: Why do espresso grains have to be finely ground and French press grains coursely ground?
upvoted_answer: Coffee brewing is simple physics and chemistry. In short, soluble compounds and oils migrate from the beans to the water. The extraction will depend on temperature, pressure and contact area between beans and water. There’s also a balance between desired and less desired flavor compounds (e.g. acidic and bitter) that a specific brewing method needs to manage, so you tweak the given parameters.
  If you have a coarse grind, the total surface area is smaller, so to get a comparable extraction you need more time (minutes for hot water as in French press, hours for cold water as in cold brew). For finer and fine grinds, you brew shorter (pour over) and probably increase the pressure (espresso).
  Of course you can also look at the problem in reverse, like in the question (“how much can method X extract”), and match the grind size to hit the optimum. However, there your assumption that e.g. an espresso machine can extract more is incorrect. The very short time plus the compact grounds means that comparatively little coffee flavor is extracted - but some would say that it’s the best parts ;-)