It's a great analogy: just look at the Mac repair shops being sued by Apple, or the idiotic things printer manufacturers and even coffee pod makers do to prevent people from "pirating" their machines.
Free software, and arguably free markets, mean free secondary markets for used goods. That includes all the repair shops and a cottage industry of craftsmen who provide those goods and services.
GNOME forks Cinnamon and Mate (active), libav vs ffmpeg (now closing), mplayer/2/mpv (mostly overtaken by last one).
Most common pattern is multiple packages solving the same problem, rather than forks - and incompatible versions.
The rest are good examples but of the millions of projects very very few are forked successfully
I could add a couple to this list as well but that does not change the fact that successful forks are exceeding rare
When my parents wireless router breaks, if I had the source code to the system installed on it I could both better understand the documentation to explain it to them, and I could perhaps patch a security problem that caused the breakdown.
There should be nothing preventing me from re-distributing the fixes, just as Sams FotoFacts used to distribute radio repair manuals, or the Chilton car maintenance manuals.
Also it's quite possible that the mechanics of a car are simpler than most software, for starters software often runs on an extremely complex operating system.
Of course its seems that that freedom is now restricted as well, but that is a fairly recent development that can be laid at the feet of the DRM advocates.
That's not recent anymore.
Also makes me fearful that we will ever be able to reform or get rid of DMCA
You have the requisite technical knowledge to do those things. Not everyone does. If someone non-technical's stuff breaks, you can't distribute the changes you've already made yourself. It limits the value of the work you're putting in and it limits the repairability of an item based on the owner's skills.
It's a bad analogy but it's as though car repair shops were illegal and you could only repair your own car. Most people would have some pretty junky beat-up cars or they'd be buying new ones every year.