I have Typekit but I dont want my system to rely on Typekit in order to run. Does Adobe not install these fonts with the apps?
Typekit fonts are supplemental to any fonts that are in your local font directory. Your system wouldn't need to use Typekit to run.
As I mentioned in your other forum post, Creative Cloud does not come with a bundle of fonts that are installed to your machine. Typekit, included in most Creative Cloud memberships, provides a library of fonts you can sync to your desktop. Any fonts that are not included in the Typekit library can be purchased for desktop from the publishing foundry.
All the fonts you purchased in the past, plus ones that got installed with Microsoft Office (many), plus any that came with pre-CC versions of Adobe software, should be on your system or in your backups.
Starting with CC, Adobe stopped bundling fonts with the software. For InDesign, for example, you only get a few faces, the ones required by the app ... 4 styles of Myriad Pro and Letter Gothic, one style of Minion Pro (Regular). All others need to be downloaded (sync'd) with the Typekit service.
More info and workarounds are in this article: http://indesignsecrets.com/adobe-drops-fonts-leaves-users-stranded.php