Can someone actually explain what the point is in installing apps for common websites like Facebook, Amazon, etc?

Convenience, for both cases. Also apps typically get permissions from your phone so they can access more data than just visiting the website.

Mobile sites are also typically cleaner and eliminate the need to zoom in for small links found on desktop sites. It makes it easier to navigate one handed especially

I asked this Q not too long ago and came to the conclusion that some people really dont know the difference (until they try to do something you can only do on your browser). It's just personal preference. I prefer the browser versions of everything over apps. I can open multiple pages to multiple sites in the browser while only using 1 app at a time.

Installing apps provides you with better access for the mobile version of the website.

Not everyone does...

I hardly ever use the browser on my phone.