Local inhibition instead of explicit k-winner for spatial pooler

Reading The HTM Spatial Pooler: a neocortical algorithm for online sparse distributed coding it appears that even though local inhibition is used it still selects the k-winners within the inhibition radius.
I was wondering if someone could explain to me what’s the benefit of doing so instead of using a smaller inhibition radius of 1/sqrt(k) (so the area of inhibition scales by 1/k).
Cheers.