One of the problem with mental health, is that it is usually not obvious for the patient (at least until a proper diagnose is made). Even if you consider some severe cases with multiple sensorial hallucinations, from the patient’s point of view everything is normal and logical.

So you are right that the wheelchair isn’t a very good analogy. Should I suffer a physical disability, I would notice it easily. On an other hand, if I suffer of some mental disability/sickness, I would have to rely on you (on other people) to tell me about the problems so that I may look for a medical diagnose and help. Yet I am not pretending it would be easy to make me notice I may have a mental problem: I would need to use my brain to find out that my brain goes wrong, that my normal isn’t normal ; and finaly find that my reality or logic doesn’t match the real one (while still being in my reality).