It's not really a Linux thing, it's a Thunderbird thing.
The equivalent would be for Thunderbird to link a .xapp file for Windows users. Good luck installing those by yourself, same with random tar.bz2s.
Of course, downloading random executables is not The Linux Way. I understand the pattern as a holdover from Windows, but it really shouldn't be the way people get taught to install software. Your distro either has a graphical package manager built in that's in control of this type of software (through their native packages or through Flatpak/AppImage/Snap/whatever) that will also keep your software updated.
IMO, distros should come with a "quick start" to explain the concepts of the software store and Thunderbird.net should default to .deb files so most people can just install it the normal way.