I am not convinced that the problem does not require inserts in sorted position. Whether or not that was envisioned was not said, but my address books have names added randomly, and I expect them back in order. A BTree is definitely the right structure for that expectation.

I would have to bench both ways for speed, but to get the full functionality that a BTree offers (most of which is very well suited to address books) with hand-rolled Perl will wind up being more complex than loading a widely used and well-optimized standard library.

Sure, a linked list is easier to roll by hand. But it is easier still to not roll by hand at all...