Everyone who is typing on a keyboard is using a mode. For instance, my "mode" is the HN comment box. Now of course that's clear to me because I can see the text appearing in the correct place.

As for the airplane example, isn't it quite natural to expect the pilots to have gone through extensive training? I understand consumer websites need to be intuitive, but highly specialized things can't really be intuitive.

One big problem with complex things like a cockpit is that the guys who build it are specialists in a different field from the guys who use it. So how are they going to know if the thing is intuitive? I would imagine a pilot mostly touches the same few commands each day, leaving most modes out of use most of the time. By contrast, the developer needs to build the whole thing.