I really don't see why there has to be women's football. It's not a contact sport and doesn't rely on absolute strength. It's not like say weight lifting or running where the top athletes are complete physical outliers in the general population. It's a game of skill where you have to have good general fitness as well. Should be a mixed sport. Anything that relies on strength or pushing the body to its limits should be segregated but anything thats skill and general fitness should be mixed.
Seriously?
Football is absolutely a physical sport, with a certain level of contact. It requires some combination of speed, power, and aerobic fitness (varying by position). Aside from the distance they run (at the top flight some players routinely run > 11km a game), every challenge for a ball requires physical power and strength. And especially when the ball is in the air - to be effective as a CB in England you need to be about 6ft2 and be able to jump >30 inches straight up (yes there are exceptions who make up the difference with leaping ability, or who just struggle in the air, but the people who are top of the aerial duel charts are this size or bigger). Hell, look at the Champions League semi final - Ajax were technically superior but couldn't handle Fernando Llorente. He picked on Daley Blind mercilessly, and Spurs imposed themselves on the game in a way that they couldn't prior to his introduction.
It's hard to find a full breakdown of the running, but this shows the distances covered by the top guys:
https://www.90min.com/posts/6299626-the-10-players-who-have-covered-the-most-distance-during-the-2018-19-premier-league-season. Bear in mind a lot of that is at high speed as well. If speed wasn't important then players wouldn't be finished by the time they are 35 (if they are lucky). Just watch some games and you can see the differences in the physical ability of the players. Especially if you watch FA Cup games - the lower league teams are usually knackered by about 70 minutes because the top players are just fitter.
Even at a low level you see this. I could compete at a certain level, then I tore ligaments in my knee. I couldn't run until a certain time after the surgery - I worked hard on my skills (and I still have most of them 15 years on), but I lost a yard of pace and a certain amount of aerobic fitness and I couldn't get back to the level I was at before the injury. All about physicality. Believe it or not, the fitness issue wasn't so much of a problem in American football, and I could disguise the lack of pace with technique, so I was able to compete in that sport for quite a few years after the injury!
In many ways, womens football can be more entertaining because there's more space and that allows the better players the opportunity to play a bit more, but it's still a physical game, just a different one.