LFS is a great learning project, I highly recommend going through it at least once.
Up one level, Gentoo / Funtoo tends to do this, however recompiling everything from source has almost no practical benefit. Furthermore, it's very often a cause of many odd issues and incompatibilities, but because the configuration is often extra special, you're basically completely on your own.
The advantages of distros is that they have smoothed most of the rough edges of making packages work well together, especially when it comes to standardized packages on production servers that you want to just work. If there are additional specific features are absolutely required, individual packages can be easily rebuilt from source on nearly every distro using their packaging tools.
For a day-to-day laptop, Ubuntu works well. I've also tried Arch as an alternative for maximum under-the-hood vs. usable *BSD-like Linux with systemd support.
Good luck and happy experimenting.