It's not all-or-nothing, though. If you need a dependency that isn't widely available on distros, then statically link it. It's fine. No big deal. But if you actually care about being a responsible maintainer, make sure you follow new releases of that dependency, and release new versions of your app (with the new version of the dependency) if there's an important bug fix to it.
If you're linking to libX11 or libgtk or something else that's common, rely on the distro providing it.
I really don't get all the anti-shared-library sentiment. I've been using and developing software for Linux for a good 25 years now, and yes, I've certainly had issues with library version mismatches, but a) they were never all that difficult to solve, and b) I think the last time I had an issue was more than a decade ago.
While I think my experience is probably fairly typical, I won't deny that others can have worse experiences than I do. But I'm still not convinced statically linking everything (or even a hybrid approach where static linking is more common) would be an overall improvement.
What also help is pacing. If your core dependencies is updating every week with API breaking changes, something like Debian is a poor choice if you don’t statically link. Some people don’t need the latest updates and are fine with security and bug fixes.
Which would be a fair reason. People who like to build things might just not want to also learn how to package stuff.