But as you yourself say, the race you competed in this weekend, there wasn't just one set of awards - there were female and male winners, as well as winners within each age group. If the female category were removed and there was just one set of "sex neutral" winners, it might not make much of a difference to you - but it certainly would make a difference to the female runners.
Also, your experience as an adult participating in a road running event isn't a good way to guage the consequences of having one sports category for both sexes, with only one set of sex-neutral awards. You have to look at the impacts this would have starting when athletes are little kids, and across all sports including team sports.
Little League Baseball has been open to both sexes equally since 1974. From 1974 to 2019, more than 11,400 boys made it to the Little League World Series - and 19 girls.
Making girls compete against boys in organized mixed sex sports is the perfect way to discourage girls from going out for most sports in the first place. Even before puberty of adolescence, boys outperform girls in nearly all sports - so starting in childhood the places on teams and winners' podiums will go almost entirely to males.
Girls will end up doing other things for exercise, as so many in the US did in the days before Title IX. And as so many girls and women have done in the decades since (when girls and women have turned out for aerobics, yoga, dance, Zumba, jazzercise, spin classes, etc at much higher rates than boys and men).
More likely, in today's increasingly sedentary, screen-focused era, making girls compete in sports against boys will mean girls will grow up not doing much in the way of exercise at all.