I have read some old works on lexicostatistics and glottochronology, like Swadesh's original articles or this work, where using Swadesh's basic assumptions, the author obtains a temporal estimation for the separation between two mexican languages. However, I am aware that later the theory received a lot of criticism for its too radically simplified assumptions, which led to some absurd result (a summary can be found here). These assumptions basically boil down to:
(1) Assumme a core of relatively estable words.
(2)Assumme the "replacement" rate in the core of stable words is approximately constant across languages.
My question is: What is the status of lexicostatistics/glottochronology in current research in linguistics? Is it completely disregarded, or are there more modern improvements that make this theory useful? I ask as a complete stranger to linguistics. A different but closely related question: In Glottochronology, starting with Swadesh's lists, as far as I know, all that is taken into account are the proportion of cognates. However, given known cognates, could the ammount phonetic changes be used too to estimate the temporal distance? This, if possible, could be one of the improvements that I mentioned above. I ask this motivated partly by this article, in which they study models for the probability of sound change and their role in reconstruction of proto-languages, but they do not mention anything about Glottochronology.