Comment Simpler alternative (Score 1) 179
There is no question that a system like Bedrock allows the ultimate in flexibility in terms of running programs from different distributions and the like. However, a multiple-distribution system like that adds a considerable amount of administrative complexity, making it relatively unlikely to be adopted by non-specialists.
There is an intermediate step that would solve much of the problem here - change the way that Linux packages are packaged and accessed so that multiple versions of library packages can be installed without conflicts, name changes, or repackaging.
The easiest way to do this would be to change the package manager to support a two level namespace instead of a flat one. So instead of simply installing the latest version of the package from your distribution, you could install a (largely) compatible version with the same name from a different source, and the package manager would pull in the necessary libraries from that source (or other ABI compatible sources) and track them as such. As long as the libraries themselves were appropriately versioned, the library packages would install without conflicts.
That wouldn't come close to letting you install any package from any distribution (in some cases the dependencies would be too complicated, or the ABI too different in subtle ways), but it would allow you to install more recent versions of most packages from the newer versions of the same distribution (including beta, rawhide, testing, versions etc) without problems in most cases, and many ABI compatible packages from other distributions as well.