Copy & paste sounds bad but what it really says is: let's make that piece an invariant and don't import the library if you only need one short function.
So I would say the trade off boils down to "simplicity vs flexibility"
In my experience, it changes neither, because the interface of the library just doesn't change. Of course it depends where you make the separation. Basically, if the interface to your library is big, you either suck at API design, or you traced the wrong boundary.
Now if you happen to only need a small fraction of a sizeable library, I can only suspect the library itself fell prey to scope creep. If there's no way to import what you need, and little more, that probably indicates a problem with the library itself.
Even big libraries which by nature must make many different things can often be separated into different components. Like the SDL for instance.
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Oh, and I was assuming we were talking about internal dependencies. Like, you write the library which will then be used in different parts of your (possibly big) project. That's very different from external dependencies, which are generally bigger, harder to freeze and harder to update.
Two components are hardly coupled just because they happen to use the same library.