I'm on 16.04 and when I click on the launcher it opens with the 6 default tabs (home, apps, documents, etc). I was wondering if I can make the launcher only list installed applications by default on the home tab. I'd like this instead of having to choose the application tab and then expand installed applications.
No you cannot. You can remove/disable the others scopes, so you don't end up using them accidentally, but the default view is always the home scope, and it's not changeable outside the source.
You can however open the apps scope directly, by pressing Super(Win)+A.
If you hold down the Super key for a few seconds, an overlay will pop up showing you several useful shortcuts like this one.