Maybe in some ways, the issue of primogeniture isn't something that should be messed with. As with the monarchy, the aristocracy dates way back into British history and in keeping the traditions and the old ways of doing things makes everything seem to have more of a sense of continuity.
Start modernizing everything to conform to today and a lot of the past is lost. Just another way of looking at something.
Off-topic, but the goal of male primogeniture was to keep the title and, more importantly, the estate (as the two
used to be linked by entailment) in the family of the last holder rather than transferring it to the family of his sons-in-law (using the patrilineal definition of family). That was done sometimes at the expense of proximity of blood, as in the aforementioned Downton Abbey scenario where the heir was a fifth cousin at the expense of the title holder's eldest daughter for example.
Male preference cognatic primogeniture, as was used in the succession to the crown in England and some other European countries, tried to reach a compomise between those two conflicting goals. When the firstborn was a girl, but she had a younger brother, the brother and his descendants had precedence in the succession over the sister and her descendants to prioritize keeping the crown as long as possible in the same dynasty (otherwise, if the female became queen and had children bearing her husband's name, a new dynasty would take over). However, if the king had no direct descendants in male line, then his daughters and their respective descendants would have precedence over collateral male lines to prioritize proximity of blood.
The purpose of male preference seems to have been made irrelevant though when royal families like the Orange-Nassaus started to keep their dynasty name even in maternal line (theoretically, the last Dutch monarch of the dynasty should have been Queen Wilhelmina). Alternatively, they could use hyphenated names like Habsburg-Lorraine, or Braganza-Saxe-Coburg and Gotha, or, if you will, Mountbatten-Windsor.
Of course, one can always argue that male preference had nothing to do with family names, but rather with a more basic belief at the time that men were better equipped to rule than women.
So if Princess Michael is known as HRH Princess Marie-Christine then Princess Charlotte's husband (should she have one) becomes HRH Prince [given name].
I don't think this will happen during QE II's reign. As someone pointed out in another forum, she prefers the current, traditional customs. But perhaps it will change under Charles or William.
That would not be a good solution in my humble opinion. I prefer a
compromise between tradition and gender equality:
1) Husbands and wives of children of the monarch should be made HRHs and princes/princesses in their own right (like Mathilde, Claire and Lorenz in Belgium for example) and could use their own names after HRH Prince/Princess .
2) In the case of grandchildren of the monarch though, only husbands or wives of the children of the heir should be made HRHs and princes/princesses in their own right. Wives of other royal grandsons who are princes would use their husband's title by courtesy (like Princess Amedeo in Belgium or Princess Michael in the UK) while husbands of other royal granddaughters who are princesses should use their own names (like Mr. Jack Brooksbank).
As implied in (2) above, I favor the
generous policy of making
all persons born as grandchildren of a monarch HRHs and princes/princesses (again as in Belgium) as opposed to leaving that titular dignity and style only to children of the heir as it is now done in the Netherlands, or restricting it to male-line grandchildren as in the UK. In other words, I think people in the same situation as Zara and Peter for example should also be princes/princesses.
I agree, Osipi, that the Princess Eugene and Prince Eugenie sound odd to us. And I have fought for civil rights all my life. But we are American and we only have a borrowed oar in the lake on this issue. 
