As far as I can tell you're only arguing against poor implementations of K-means. If you demand that the score strictly improves at each iteration then the algorithm must terminate.
I saw your mention of Knuth elsewhere, I looked it up and he demanded that
> An algorithm must always terminate after a finite number of steps ... a very finite number, a reasonable number
This is a pretty niche characterization and almost certainly not what the original post was asking for. However, I concur that there is no guarantee on how quickly K-means terminates or on how good the output will be,. But... if you're going to be that strict about it you would even have to rule out the Simplex Algorithm, which everyone I've ever spoken to thinks of as an algorithm.