The goal of e-means is to be a drop-in replacement for k-means. It solves the exact same problem, with the exact same inputs and delivers better centroids and quality in a fraction of the time. So I'm not sure what we get wrong by working on a problem that hundreds of papers also worked on. Is the whole k-means literature getting it wrong then ?
Picking the k is a separate problem, on which also a body of literature has worked too. e-means is a drop-in replacement for k-means so you can use any method you would use for choosing the k but with e-means instead of k-means.
e-means performs better on a very wide array of datasets, definitely not degenerate cases, don't hesitate to check out our paper at https://arxiv.org/abs/2611.09501.
If you have any question or objection, I'll be happy to answer.