Then you'd judge some smart people as not-smart, possibly to your detriment.

Ignorance is not opposed to intelligence. Arrogance is a flaw that can reduce the benefits of being smart, but it doesn't make someone not-smart.

(Unless you're using 'smart' differently to the conventional meaning, which is an unhelpful thing to do.)

You need a certain level of arrogance to think that you are right despite everybody thinking you are wrong. If you are threading new ground, you need it to succeed. For example, all those startup creators are arrogant. They think their ideas will succeed despite knowing that they have 99% chance of not succeeding.

Your reaction is an irritating trait of our western societies. Almost all our hero figures, all our geniuses, are arrogant assholes. Almost everything on TV is about a guy winning against all odds, our business geniuses had all crazy business plan, ... Yet, we despise the same people if their plan does not succeed.

Take a guy like Zuckerberg. Drop out of school to build your startup with borderline illegal business tactic, that's genius. Do the same and fail and you are an obvious loser that deserved what he got and should be happy not to be in jail. This mixed signal the society is sending is annoying.

Then many of the top researchers in the world (even including nobel prize winners) do not meet your definition of smart.