We did this when I worked on factorio (on all three desktop platforms, not just linux), it works really well. Side bonus is you can make the inevitably required small tweaks inside the library easily because it's all integrated in the same build system as the rest of your game.

SDL2 will even allow the user to override the static library and substitute their dynamic copy at runtime, so even though you distribute it statically you don't lose out on the advantages of updates.

...why don't all libraries work that way?

This is not a good idea because SDL can get fixes down the line to be more compatible with changes in desktops. I have a bunch of very old games on Linux using SDL 1.2 and whenever they bundled their own version pretty much never works, but i can easily fix that by deleting it and letting the game use the system provided one.

And TBH i'd rather games just assume SDL or is available and have it part of the system requirements (they already have other software requirements anyway), perhaps with a tiny launcher that tries to load the library dynamically and if fails it reports a more user friendly error. Most gamers on Linux will have it installed anyway since they'd be either launching from Steam (which bundles it as part of its own runtime) or also have other games installed.

(sadly SDL2 breaking ABI backward compatibility with SDL1 puts a wrench to that idea, which is why personally instead of using SDL2 i just write my own code - e.g. SDL2 fullscreen mode doesn't work in many window managers)

I agree, for their use case they should have linked to SDL2 as a static library. It was the best option instead of patching the binary with patchelf.

I think many developers don't know about static libraries. For some reason they think they have to use a shared libraries. This is probably due to many tutorial saying something like: download the SDL2 library from there, it is provided as a shared library, here the instructions to use it with Visual Studio.

The way I do is with static libraries, I ship a single executable, all the third-party libraries are linked in as static libraries. The only dynamic libraries the exectuable will use are the standard libraries that are part of the OS.

I do this very easily with the help for lhelper:

https://github.com/franko/lhelper (I am the author)

that has recipes to build many libraries including SDL2. It builds the library on you system using your compiler and your settings. By default it will build static libraries so you don't have to bother distributing additional dynamic libraries.