Sorry, but this is the very example why butterflies have to be considered.
In 1813, Charlotte, the Princess Royal, was not even married and obviously not dead, so all her uncles were not married either - including the Duke of Kent.
The battlefield death of her uncle might change a lot. In two years, Charlotte might find another prospective husband than Leopold. She might marry a bit earlier or later, and the pregnancy might occur later or never at all, or run a different course. She might survive much longer than 1817, or at least her child might survive as royal heir.
All this might completely change, postpone or remove the scramble for brides among the other sons of George III.
Kent might marry someone else. perhaps the Prince of Leiningen lives a couple of years longer, so his OTL widow Victoria is not availabe for Kent. Anyway, there are 1:1 odds that the first child of the Duke of Kent and his wife might be a boy. Or the marriage might remain childless.
We are not just talking about concious decisions but also about natural processes nobody could have influenced. Simply stating "everything happens as in OTL" is not remotely plausible.