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.
Even if I get a tarball on OSX I can double click on it and then drag the application into the "Applications" directory or run the installer. I'm not sure why this is so challenging on Linux.
Linux distros have a complex network of dependancies, config files, and general crap that requires sophisticated tooling to manage which is different on different distros. All to save a few kb of storage space.
The real reason macOS and Windows are easier to distribute software on is because there's only one Windows and only one macOS. "Linux" is not an operating system, Ubuntu, Arch, Fedora, RHEL, etc. are all different operating systems that just so happen to share a kernel and a similar ecosystem of open source software. So compatibility between them is more of a coincidence than anything else.
Luckily nowadays we have Flatpaks and AppImages, which both solve the problem of simplifying app distribution and installation universally for all distros. Although devs will probably get a lot of hate if they only distribute their app as a Flatpak or AppImage and don't also offer tarballs/debs/rpms...so app distribution is likely to remain complicated for a while.
All without opening or requiring the user to open a hideous terminal just to run the app.
> I'm not sure why this is so challenging on Linux.
Desktop Linux fundamentally can never solve this problem. All of the packaging alternatives of alternatives have created a mess and confusion around which distro can open what and not only these alternatives even work out of the box, there is no guarantee that all Linux distros will be supported for that.
At most it is a 'solution' creating a new problem; whist still looking for a problem to solve.
You... kind of are though, to the extent that what you tried wouldn't work on Windows either (equivalent to trying to run a program in a zip without extracting it). Extract the directory and run the thing called thunderbird in it.