And Thunderbird could just as well give you a .deb file if you're browsing from Ubuntu or a link to whatever software library your distro uses.
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.
The equivalent would be for Thunderbird to link a .zip file for windows users, which is actually a pretty damn common way to distribute software (or at least it use to be) so that you don't need to be an admin to use it, and would have the exact same feature of having random dynamic libraries and stuff like that sitting in the folder.