I have had a hunch for a while now that (in addition to these tools), Anthropic has actually leaned in to Claude's distinctive manner of writing since it makes the text more obviously AI generated and thus less susceptible to misuse.
That's not necessarily the same thing as a markov-style fingerprint but it could be a correlated factor.
It's pretty trivial to command it to not speak that way. That's one of the first things you should write into the prompt. What style you want it to write in. Make it use a very concise and dry academic style with no overt LLMisms, melodramatic or flowery language, or metacommentary.
I had a similar thought but I assumed they leaned in because it improved performance on coding or something like that