Am I wrong to assume that these Ubuntu instructions would work for other Debian like systems such as Raspbian?
It's not the difference between Ubuntu and Debian and Raspbian; you can install Ubuntu or Debian on a Pi if you want, but those instructions will than not work any better then they did on Raspbian.
The problem is the type of CPU. Executable code ...
If I follow your commands, first I get an error massage tar: /usr/bin/icecat/installed: Cannot open: No such file or directory. First I had to create it with before unpacking the archive:
rpi ~$ sudo mkdir -p /usr/bin/icecat/installed
rpi ~$ sudo tar -xvf icecat* -C /usr/bin/icecat/installed
Now if I look at icecat with file I find:
rpi ~$ file /usr/bin/...
There is no etcher release for pi. If you want to flash the memory with OS you need a windows or another raspbian activated raspberry pi. Then try this command(if you are using a linux)
sudo dd if (path to image) of (path to device)
I this way ou can make a flashable image.
To answer your permissions/folder question: you need root permissions for /usr/local/bin because that folder belongs to root, and the reason for that is that the root user has that directory in their $PATH.
If /usr/local/bin was write-accessible to anyone, a malicious user could create a script there named as a common typo, such as cd.., or a common command ...