Speaking as a former Apple employee, and long time Apple platform developer, Autodesk is doing this wrong. I won't argue about the Library thing.
If you want a simple, installed in the correct place version of Fusion 360, download it from the MacApp Store. It's there, a bit behind, but there. It installs in the right place, and it doesn't do anything evil.
First, putting things in the dock is not something you should be doing. The Human Interface Guidelines are pretty clear. And it's evil. 🙂
That's what Fusion should be doing. Putting a link into Applications.
Again, I'd need to check a vanilla install of Mac OS, but do this, even if you have to type in your password.
There is nothing preventing Fusion from installing in /Applications and self-updating. Many applications do that using the Sparkle.framework.
I would love to see Autodesk put the time in to properly package Fusion 360 as an application for the Mac and follow the conventions. Adobe does. Microsoft does.
I understand the potential wait in the MacApp Store queue could be an issue for an emergency fix, but there are procedures for that. And those apps can automatically update in the background (so you aren't launching and then waiting for the upgrade to install so you can restart). Packaging it is a pain, but they do it for a number of other Autodesk apps.
The VERY first thing I do when I get a new copy of Fusion is Select it in the finder and control click or right click on it and "Show in Finder". Then I Command Option drag to /Applications This should give you the little arrow cursor, to make a link. Drop it into Applications.
I added a quick capture video of how to do this. (I really time compressed the launch. 🙂