There's not really much in the way of photography schools (anymore), as per your definition. Just like there's not really much in the way of painting schools, sculpture schools, or poetry schools. I guess there are some famous music schools, but even most of them teach more than just music (Julliard is also a top dance and drama school, for example). So most REAL photo schools are better thought of as art schools with a strong photography program. And there are a lot of those in this world. Most of the photographers you will find in a major museum will likely have attended one (or more) of them. Many may have studied something other than photography in school, but that's not uncommon among artists. Most good artists excel in many mediums, and many will switch mediums throughout their life. Art schools, and universities in general, don't really teach you technical information you need to do a job. That's what trade schools are for. Art schools and universities tend to teach you new ways of seeing, listening, and thinking about things.
The internet is a terrible place to learn stuff like that due to the massive amounts of bad information. If you don't know any better, good and bad information both look the same to you. The internet is great for learning simple stuff though, like the exposure triangle. That's something that only takes a few minutes to learn. But for more complex ideas like composition, color theory, and visual language, you're going to need to devote several years to get a firm grasp on those things, and with all of the bad information on the internet out there, it's just not a good medium for that kind of education.