It is much easier to just use standard package format (rpm/deb/apk/etc.) and standard installer (yum/dnf/apt/apk/etc.). Of course, you can invent your own build and installation system, it will work too.
That depends on a lot of factors. The advantage of an approach like this is that every package is built in a clean-room container independent of the host. For example my host is os x and I'm building binary tarballs to run on ubuntu. If you have a build server obviously this is less of an issue.
Just build .deb's instead of tarballs. Use "alien" to convert .tgz into .deb, for example. I see no reason to invent my own build system, package format and package management software.
I build my rpm packages in clean room chroot (using mock) for about decade. It works fine in docker too.