Computational Efficiency of Periodic Boundary Conditions
The application of periodic boundary condition does not mean that the system is explicitly replicated. You only deal with the particles within the unit cell (the box that you replicate), but you let them interact with the replicated ones outside of this unit cell.

Consider a simple 1-dimensional case with three atoms in the unit cell: $\ce{A-B-C}$, and lets assume we only need to treat nearest-neighbor-interactions. So the "monomer" has only 2 interactions: AB and BC.

One option to simulate the macroscopic system would be to explicitly deal with $\ce{A-B-C-A-B-C-A-B-C-A-B-C}$ (or even longer), but this requires a lot of atoms with accordingly many interactions between them. And even then both ends of the chain would be missing one neighbor.

Using periodic boundary conditions, one explicitly treats $\ce{A-B-C}$ only. But this time we will allow $\ce{C}$ to interact with $\ce{A}$, since the periodic boundary conditions implicitly tell us, there is another $\ce{C}$ to the left. Similar, there is an implicit $\ce{A}$ to the right of $\ce{C}$. Compared to the monomer from above, we have again 3 atoms, but now there are 3 interactions to be considered: AB, BC and AC.