It's not only Wentworth, Captain Benwick is also there: a naval captain and a father of young children. You'd think he would have seen the odd head injury in his time.
It is supposed to showcase Anne's comptence and reliability when everyone else falls apart, and it's the turning point of the novel when Wentworth realises that the ideal is a midpoint between being too easily persuaded and being too headstrong, rather than what he'd previously been idealising which is doing what you want no matter what anyone else thinks.
I wonder whether the men falling apart also shows that they really don't have a clue about women. You see the men across JA's books express many variations on the theme of considering women as irrational, over-emotional, unable to make decisions for themselves. Quite a lot of the women have to explicitly make the point that they are actually fully functioning human beings and not some lesser race. Even Wentworth's own sister says to him 'I hate to hear you talking so [...] as if women were all fine ladies, instead of rational creatures.'
Partly it's true that women were expected to eat less, wear restrictive clothing (although not as restrictive as earlier or later styles), and generally be delicate, which does then have genuine health impacts. Witness the fact that Fanny Price is made ill by not being able to ride a horse every day and having to walk in the heat of the day instead. Jane Bennet needs an apothecary and several days' bed rest after a walk in the rain. Marianne Dashwood nearly dies from walking in damp grass and hanging around in wet socks afterwards. None of them have infectious illnesses, which are a whole other category of health risk. All of them, IMO, could have been avoided by building up a stronger constitution through a good diet, comfortable clothing etc. Long and short of it is, you treat women as delicate flowers and that will actually have an effect on their health, and then you don't know how to react because women are such delicate flowers. It's circular. It's notable that, with the exception of Fanny (and possibly Catherine in NA), the main heroine of each book doesn't go in for fainting fits and catching cold because it's a bit damp out, they're usually the more sturdy and sensible ones. I think JA is trying to balance showing that women are stronger than people give them credit for with the reality of living a restrictive lifestyle, which does make people ill (and without germ theory and a lot of other modern science, so the idea that you could get fatally ill from walking in wet shoes was perhaps less ridiculous).