Your fingertips give you feedback about the pressure you're applying, but they don't give you feedback about the desired outcome of the task. If you're drawing then you get feedback immediately - that line was darker or lighter, thicker or thinner, trailed off in this way. You can see it on the paper and that's associated with the feeling you get via your fingertips.
While I agree that most people would understand the concept of pressure sensitive interfaces. It's not clear to me that people have much practice with them, nor that what little practice many of them do have equips them to be particularly skilled with the things.
By way of illustration: can you imagine someone who hasn't learned to use a computer before learning on an interface such as this? It's hard enough reminding people that you choose the right mouse button to access particular parts of the interface, now you have to remind them that you press this button but only this hard (how do you even give them the knowledge of how hard to push to access the damn thing?) And it's not particularly discoverable, a lot of people don't even discover the right click menu for themselves, when there's a button just sitting there for them to press to find that out.
I don't think it would occur to people that the system would be expected to function in that way. Most of our tools don't seem to. Those that do manage to do so, and to do so well, seem to have extremely short feedback cycles between the use of input and the desired output state of the activity.
It's possible that you might make a menu fade in, as someone presses harder on the screen to try to shorten the feedback cycle. That would make it more discoverable and allow people to work out how hard they need to press. The problem there would be that the menu would start showing up during routine use, (because if you made it only show up when someone pressed hard, it would have the same limitations of being on discoverable as the other system had.) Perhaps people would just get used to such a system, but I can see it being extremely frustrating to have a menu fade in as you were scrolling through a web page.