I grew up IN the east coast vs ON the east coast

It's completely straightforward.

"West coast" does not literally refer to the strip of beach - it means places like nevada, sacremento, fresno, etc. It's one of the (vaguely defined) "regions" in the US .. like "the south" or "midwest" or 'bible belt" and so on.

The fact that: if you take a phrase, which has grown to have a common meaning, literally, then it is confusing, funny or whatever: so what?

If you asked "Do people who live on the bible belt live on a strip of leather??" the question would probably just be closed!

This is an interesting question. I wouldn't say that I live on America when I live in America. However, I would say that I live in New York, vs. on New York. I stood in the Empire State Building has as clear and as different a a meaning as saying that I stood on the Empire State Building. In the former I could have been on the 26th floor and in the latter it is clear that I stood on the roof.

Does size or location matter more? I would say that I live on Planet Earth, in North American, in New York, on Hazel Street, in a house, and am sitting in a chair. But you could say you sat on a chair as well. It would seem that the word, in, has a lived-in, actionable sense, whereas, "on" seems more passive as well as dwelling on the surface. I worked on a farm, and fell in the pigsty. In the case of chair, the chair I sit in at my desk where I write, I would say I sat my butt in the chair and wrote for two hours, vs. I sat my butt on the chair and wrote for two hours.

This is more of an exercise in logic than anything.

According to the Oxford American dictionary:

Coast - The part of the land near the sea; the edge of the land.

This suggests that one grows up on the coast, rather than in the coast, since the latter would indicate being raised inside a piece of land. Usage statistics also support this conclusion, as "on the east/west coast" is significantly more popular than "in the east/west coast," according to Google Ngrams.

You live in the desert. You live in the mountains. But, you live on the prairie. You live on the (east, west) coast. We were looking for instances where the "vaguely defined regions" didn't apply to using "in."

It really depends on common usage around the headword. All of these are common usage:

I live in the east.

I live on the east coast.

I live in the east coast city of XXX.

I live on the outskirts of the east coast city of XXX.

I live in the suburbs of the east coast city of XXX.

We tend to use on for lines or borders between areas (hence on the border).

Note: I have a house on Lake Como (it's not actually on the lake; it's on the line around it).