I'm guessing you're downvoted because your implied solution is no better (and arguably worse) than parent's "unless you jailbreak". Regardless, it's not a solution for "normals":

1. Download and install Xcode.

2. Find the source code for the application you want. You know GitHub works, right, Grandma?

3. Compile, sign, and deploy to your device. Assuming it built without error, that is.

4. Aww, shit, Apple's signing process is still a hot mess. Best get to Googlin' on those validation errors!

Generally, those that go down this path use a much more streamlined solution like downloading an IPA file and using something like Cydia Impactor (http://www.cydiaimpactor.com) to sign and install the app. It least, I think that that's easier than finding a kernel bug in iOS…

Do you need to pay Apple for a Developer ID in order to be able to do this?

Nope! You don't even need to be on OS X. You just get limited by the 7 day signing period if you don't pay.

Nice :) Does it work with Linux or is “not OS X” only Windows?

Works with Linux. Binaries at http://www.cydiaimpactor.com

Does a developer license get you more than 7 days?

Yes.

No, you can do this with a free license as well. Impactor basically automates the tasks that Xcode's doing when it installs apps.

It's still a valid solution is all. And there are tools available to make it easier for the "normals" as you call them. http://www.cydiaimpactor.com/