Opening a pdf inside a browser feels to me like an application inside an application. My brain can't handle that load. I would rather have the browser to browse the internet and a pdf reader to display pdfs. If I clicked on a link to a pdf, it is _not_ part of the web, and I want the browser to stay out of it. Same goes for Office 360 wanting to documents inside my browser. I don't want it to do that. I have the necessary apps installed for it.
> the vast majority of websites these days fully fledged applications
Many apps do exist on the web. Not many of them are very good, PDF is a bit case in point - web struggles to fully implement PDF read/write (partly a complexity thing, partly I'm sure a tactic non-compete with Adobe).
Even more sites still exist that aren't apps, even if a few big sites have stolen people's imaginations...
So two reasons why you don't really want your PDF in the browser (I don't mind much if I'm never going to look at it again but otherwise no I don't want it in my browser).
Even if the first two weren't true, there's still just the fact that, no, PDF is local, web is not. I don't need an internet connection for one, and I don't need to worry about one messing with the other. Sounds like a strange thing to worry about, but browsers do crash, and more importantly browsers are often filled with tabs. You can have many PDFs open but you don't need to keep them all in memory...
I didn't mention any particular sense about application inside an application. I did say how it "feels like to me" and how my brain fails to handle it. There is a clear shift of modes when I click on a link on a website and suddenly the contents of the current browser window are replaced by a pdf with its own back and forward buttons, its own page layout, its own toolbar and so on. If it stopped feeling different like that, I would not even notice it and wouldn't even bother to find out if what I am seeing is a pdf or an html based website.
I really would not like to ruin the entire internet for you, but isn't the vast majority of websites these days fully fledged applications, hence applications in application in the sense you mentioned ?
I would argue that a pdf reader is much simpler than multiple very popular webpages nowadays.