Height is an objective and one-dimensional measure. It measures your ability to do a single thing: reach objects that are farther off of the ground.
I think we really do humanity a disservice if we define intelligence that way. The brain is capable of so many other things.
Surely you have known people who were bright (or brilliant) in some areas and lacking in others.
But for people who I would consider as intelligent, it's not a result of just knowledge. Or just skills.
I would trust their ability to "get" concepts they've been previously ignorant of relatively quickly. The wheels just spin faster.
And a lot like height, there's diminishing returns and what not. I can get a step ladder, then being tall is just a fact. Being intelligent can help you get a concept quicker, but once we both understand it, there's no effective difference.
But no one gets defensive about height. Or strength. Or anything with visible qualifiers. Which is funny, because intelligent people are better at thinking in the abstract and intelligence and the results of it are abstract.
People get really defensive around intelligence though. Everyone wants to be at least average if not above average. If they can't claim it in one area, they'll try to redefine intelligence to include themselves. And we do have the habit of mistaking institutional knowledge for intelligence.