I'm curious on which Linux did you encounter issues while installing Docker? I cannot comment on the (to me somewhat pointless) Docker Desktop GUI installation on Linux, but I can confidently report that installing and using docker engine on Ubuntu, at least, is quite trivial and clearly documented[0] on the website.
It also seems like Docker is now able to run rootless as well, so my nitpicks are actually more minor than I originally thought. It's still not daemonless, but it would work for my use case still I think.
I use CentOS, Ubuntu and Arch and have to regularly use third-party repos, PPAs or the AUR - this isn't a particularly uncommon thing to do when installing software. And it beats running a shell script, which is how k8s stuff works most of the time :P