The approach of Bedrock Linux is very interesting. It makes use of Linux-specific features like bind mounts and tries to unify several linux distributions into one meta-distribution, which gives the framework for the multi-distribution operations. They could also use namespaces for a more strict separation of clients, but that's a detail.

The idea to move completely to musl is a little bit utopistic, because musl libc is in a very early phase if you want to compile any piece of software of the base system with it. It's mostly C99/C11 and POSIX compilant, but there are several GNU-specific libraries missing, and in a world which uses GNU userland on Linux it's not simple to overcome that limitation.

The mentioned /etc problem seems to be the same problem as solved by ip-netns(8). Take a look at the source if you need further information, it's based on other bind mounts.

But I don't think Bedrock Linux is the next-generation approach for Linux distributions, or rather software distributions in general, though they don't claim that. I'm working on my own Linux distribution since about a year and it's based completely on a ports tree, as known from FreeBSD, but with a simpler code base and simpler Makefiles. At the moment, I'm trying to create a stable commit, which will build without issues in several configurations, but that's hard work, especially because Linux or rather the Linux userland is mostly a ghetto™ (you won't get information about much low-level software).

But I think, as you should noticed, that Bedrock Linux has a right to exist, but it won't be the next-generation approach.