Here are three things I think, and they have in fact nothing to do with Rust:
1. The easier it is to add dependencies, the more dependencies will be added on average - unless you work purposefully against that.
2. The effect of a rising average number of dependencies in libraries is that their number of dependencies grows as well, and the number of their dependencies' dependencies... up to dependency graphs of several hundred nodes size. Like in exponential growth. An example would be the dependency graph of jquery.
3. I observe this "exponential" growth can have chain-reaction-like effects, like if you have a mass of U235 that achieves critical mass. Below that critical value, some neutrons flying around might trigger a few fissions, but these die out. Above that value, neutrons lead to fissions which lead to more neutrons and so on. The same can happen with complexity in multi-component software. At some point, complexity goes through the roof.
And the latter is especially true if backwards compatibility is not strictly observed, since backwards-incompatible changes tend to be infectuous in that they often make their client components (parents in the dependency graph) backwards-incompatible as well, in other words, there is breakage that propagates up the dependency graph. That breakage might die out and be able to be contained by local fixes, or it might propagate. And once your dependency graph becomes large enough, it is almost guaranteed, that you have breakage.
All these things together is why I believe that systems like NixOS or Guix are the future (but of course there might be other developments in that space).