Only people engaged in active buying and selling set the price of Tesla stock. It's called "price discovery." Any institution such as an index fund passively holding stock does not effect the value of the stock, so the percentage of institutional ownership doesn't itself matter.

Institutions are organized people. They aren’t more immune to the information firehose than me or you.

That's pretty normal for a company like this. Also, let's be honest, based on historic data, it has been a good investment.