Responses
This was very common in the time period this is depicting, mostly female but also for first-born males. It is all about progeny. The "prettiest" lady is probably sixteen, no older than twenty. Once she has been introduced to society, her clock ticks and her time is up shorter than a man's. So attempting for a husband would be seen as her doing what is expected of her while for the duke, going to war is leaving a responsibility unfulfilled. He is also in a high position of power so without an heir, the seat could be contested and even start a war of its own should he die.
I like the series so far, but I think it's ridiculous and hilarious that the only "flaw" the duke has is that.... he's single? Really? How is that a problem when clearly he could get any girl he wants and multiple girls try to flirt with him all the time. Even the "prettiest" lady at the ball approaches him (and somehow she's not mocked for being single as well?)
It is just such a silly and forced attempt to give the ML flaws, I couldn't help but laugh.