I would love to hear some examples of US Presidents and their families being involved in the sort of examples I quoted you, that is leading from the front, not from a desk. I don't doubt they did it, I just can't find reference to any.
The relevant comparison would not be PM's as they are not head of state and we have only had PM's for a few hundred years, we have had monarchs for 1200 years as England and some 3000 years before the regions became one nation.
Off the top of my head, Washington, Lincoln, Grant, Teddy Roosevelt, Truman, probably Eisenhower, and Kennedy. At the time, the were unit commanders rather than President. Which is why the PM is indeed the relevant comparison -- a purely ceremonial status as "head of state" doesn't matter, the fact of being elected at some point in life rather than born to it does. Also the shortened timeframe makes them a better match, since with US Presidents we're talking about more or less modern warfare.