I will divert if the wx drops below the limit and I don't have an alternate from the missed approach. I know it would be annoying but that is the intention of the rule in my opinion.
I do about 700 hours a year and have never had to do it in the last decade that I can recall so it's not a big imposition.
For you to be airborne without alternate fuel, and the wx dropping to the extent that an alternate is required on destination, something unusual has happened either with the forecasting, or your decision making at the pre-flight stage.
Sometimes due payload/ destination combinations it is on the cards to have to bug out at top of descent but it hasn't happened to me yet.
If you began your descent and threw away your opportunity to divert somewhere suitable and the wx ( which has already been incorrectly forecast) continues to deteriorate then I think you'd have a hard time explaining your decision not to divert.