Literally from that page

The coastline paradox is often criticized because coastlines are inherently finite, real features in space, and, therefore, there is a quantifiable answer to their length.[17][19] The comparison to fractals, while useful as a metaphor to explain the problem, is criticized as not fully accurate, as coastlines are not self-repeating and are fundamentally finite.[17]

Which a physical space cannot fulfill

Coastlines exist in the real world, they are by definition finite structures. You can only zoom in to them so far before the structure is no longer a coastline.