Thank you for your opinions and insights guys
What I experienced a couple of years ago was something similar (diversion was executed due to unexpected fog (nothing on the TAF at all) at destination with ILS U/S that day) to my example except that, after having chosen the best weather alternate, second or third commercial option, I don't remember exactly, during the 20 min trip to that the visibility and RVR dropped quickly there too.
The TAF was giving this conditions later (something about 2-3 hours later) and the reports we had at the beginning of the diversion was good (something like 5000 mt and BKN 020).
We ended up conducting an autoland due to fog, something like 600 mt RVR and BKN 002 but at that time we couldn't change our plan.
I know it's "one of those days" where you can't actually count on precise weather forecast and we needed an autoland anyway, but what it surprised me was that others were going straight to the best commercial alternate even if it was already close to LVP activation (Low visibility procedures) at the start of the diversion.