That's definitely a solution, but it comes with its own problems, in particular that you add a significant dependency on what is essentially a middleman organisation trying to manage all possible dependencies. This doesn't scale very well, particularly because there's a kind of M×N problem where M packages can each have N versions which can be depended on. In practice, most distros tend to only support one version of each package, which makes the job easier for the distro maintainer, but makes things harder for everyone else (library authors get bug reports for problems they've already fixed, end users have less ability to choose the versions they need, etc).

In particular, it also makes upgrading a much more complex task. For example, React releases new major versions on a semi regular basis, each one containing some breaking changes, but not many. Ideally there wouldn't be any, but breaking changes are inevitable with any tool as situations change and the problem space becomes better understood. But because the NPM ecosystem generally uses locked dependency lists, end users can upgrade at their leisure, either with small changes every so often, or only upgrading when there's a good reason to do so. Both sides can be fairly flexible in how they do things without worrying about breaking something accidentally.

Under a Linux distribution model however, those incremental breaking changes become essentially impossible. But that means that either projects accumulate cruft that can't ever be removed and makes maintainers' and users' lives more complex, or projects have to do occasional "break everything" releases a là Python 2/3 in order to regain order, which is also more work for everyone. There is a lot less flexibility on offer here.

I don't think these sorts of problems disqualify the Linux distribution model entirely - it does do a lot of things well, particularly when it comes to security and long-term care. But there's a set of tradeoffs at play here, and personally I'd rather accept more responsibility for the dependencies that I use, in exchange for having more flexibility in how I use them. And given the popularity of language-specific package repositories that work this way, I get the feeling that this is a pretty common sentiment.

What happens when your distribution only have old versions, or worse, no versions of the libraries you need? You hoop distribution? You layer another distribution like Nix or Anaconda over your base distribution? You give up and bundle another entire distribution in a container image?