World War 2. He was the Prime Minister of the United Kingdom, given authority to be the Commander and Chief of their armed forces.
Churchill is not a good example for this. He participated in strategic decision-making, but as the leader of what was ultimately a secondary member of the United Nations, and many of his most famous strategic decisions were bad. To take the Second World War as an example, Churchill's focus on the 'soft underbelly' of Europe - the Mediterranean littoral, one of the most mountainous regions on the continent and a tertiary theater at best - was probably detrimental to the Allied war effort. His focus there was probably a combination of bad strategic logic and a focus on British influence and empire-building to the detriment of the Allied cause.
Churchill also exhibited poor strategic decision-making while First Lord of the Admiralty in the First World War. His bureau was poorly run, with few systemic processes and a great deal of personal conflict between himself and his military colleague, Sir John Fisher, the First Sea Lord. The efficiency losses due to this personality conflict and management failure undoubtedly inflated British losses and weakened the Royal Navy's performance in the war. He indulged in bizarre political theater at the expense of sound and sane management when he attempted (and failed) to personally lead the Royal Marines to the rescue of Antwerp in the fall of 1914. And the Dardanelles expedition, though responsibility for it does not rest solely on his shoulders, was an expensive catastrophe with virtually no chance of meaningful success.
These are not solely my opinions. Many historians have stated them before me. Hew Strachan, a relatively sympathetic historian who also served as a general officer in the British Army (and is now one of the foremost authorities on the Great War), concurs with much of the literature of the last several decades on Churchill's management skills. Naval historians like Stephen Sondhaus and Paul Halpern have much the same to say about Gallipoli. And condemnations of Churchill's "soft underbelly" strategy have been emanating from America since 1942.
Obviously, British forces under Churchill's ultimate authority secured numerous military successes, especially in the Second World War. But, as Ridwan points out, it's not clear that victories like Alam el Halfa or Imphal can be laid at Churchill's feet rather than those of the British commanders and soldiers who actually participated in those engagements.
So practically every historical and military scolar is wrong? Okay then.
But fine, I'll use another example from World War 2: Joseph Stalin. Go on, tell me how he didn't lead the Soviet forces.
Stalin, however, is a much better example.
No one can deny that Stalin's position of military leadership in the Soviet Union was active and thoughtful. He led the Stavka and did not merely preside over it; all critical military decisions ultimately went through him. More than any national leader of the war - save perhaps Jiang Jieshi - Stalin involved himself in the nuts and bolts of military command.
Many of the war's poorest military decisions can be laid at his feet. Throughout the first several years of the war, Stalin repeatedly misjudged the combat power of the
Wehrmacht after a defeat and rashly ordered counterattacks far too early. His orders badly overextended Red Army forces time and again, leaving them vulnerable to German ripostes - at Smolensk in the first months of the war, then again during the winter counteroffensive of 1941-42, again at Izyum in the spring of '42, at Third Kharkov in '43. He and Zhukov developed a monomaniacal fixation on the German Army Group Center that cost the Soviet Union dearly: in 1942, they devoted most of the Red Army's mobile units to defend the approaches to Moscow, leaving the southern front poorly defended just in time for a massive German attack, and in the winter of that same year, Stalin authorized and supported Zhukov's MARS and JUPITER offensive that turned into one of the USSR's greatest military disasters of the war. And all this came on the heels of his decision to gut the Red Army's officer corps shortly before the war broke out with his purges.
But Stalin also made many more decisions that turned out much better. He weeded out poor commanders and backed good ones. The Stavka and high command he built, by 1945, possessed a crop of superb leaders: Vasilevsky, Rokossovsky, Katukov, Malinovsky, Purkayev, Meretskov...even Zhukov and Konev. Several of these men had been purged before the war; Stalin brought them back, because he recognized and needed their skills. In a more specifically military sense, Stalin reinforced success rather than failure on the front lines, too. He did not throw good money after bad (especially after 1942); offensives that had petered out were ended, while successful ones were lavished with more troops, arms, and supplies. He also provided a moral effect that, like much leadership, cannot be quantified in a meaningful sense. It is hard to imagine the resistance that the Soviet Union offered in 1941 and 1942 without Stalin's presence.
Because, this debate started about military leaders. None of the people you mentioned are conventional military leaders other than the rank their offices automatically gave them by default or that they assigned themselves. They're the Steve Jobs of WW2. Telling their generals to win the battles, and they do it, but they get the credit.
One could make the same complaint about generals; rarely do they personally participate in the battles that their troops win for them, and subordinate leaders do most of the work of creating the plans that are actually implemented.
But anyway. Being physically fit is hardly a requirement for military skill. One could look at actual army commanders with the same critical eye. For example, until recently, it was customary for many higher-ranking generals to be very old and still exercise command of their forces. King Wilhelm I, who commanded the Prussian army in the war of 1866 and the united German forces in 1870-71, was aged 69 when he won the Battle of Königgrätz, and 73 at Gravelotte-St. Privat and Sedan. By the time of the Wars of Unification, he was not a young man nor a particularly fit one;
this is a period painting of him at Sedan accepting the French surrender. Wilhelm was present on the field for all of the great battles of those wars, and physically participated at Gravelotte-St. Privat by riding into a mob of retreating troops, whacking them with the flat of his sword and swearing at them to return to their posts. Never mind that he would be utterly helpless in a wrestling match with the average Imperial Army
grognard.
Hell, if I went back in time to 1944, I could probably destroy Vasilevsky or Marshall (or Eisenhower, or Zhukov...) in any physical-fitness contest you care to name. And those were only the guys most responsible for winning the biggest war in human history, so, yeah.
Nowadays, it's rare to find soldiers, even high-ranking commanders, in quality Western militaries that aren't physically fit, let alone people who, ah, let themselves go. Part of that is down to regulations and peer-pressure, and part of it is down to the inculcation of the idea of the general remaining a soldier regardless of rank and grade, and part of it is down to a general modern recognition of the value of physical fitness.
But it'd be ridiculous to expect the likes of H.R. McMaster or James Everard to be able to match pull-ups or five-mile run times with staff sergeants, let alone spar with Mayweather or Rousey. They're more fit than the majority of the population, and they're probably above-average even for their respective militaries, but their jobs don't involve being meatheads. Usually, the idea is that the Old Man - or, y'know, Woman - can show that s/he's "still got it", but that's a long way from being an Olympian.
So it's preposterous to say that the difference in
peak physical condition between the strongest men and the strongest women would have
any bearing at all on the suitability of women for higher command. It's just not a relevant factor.