…no.
The arguments for why high school sports, IE the collection of official sports teams representing high schools at competitions across the country, should be segregated by sex all involve the argument about competition, because that is what the collection of entities we can high school sports are.
No one is talking about PE when they’re talking about high school sports.
What you’re talking about is divorcing high school sports from educational institutions, and then having everyone participate in what we currently call “Physical Education” instead of having PE for some and being a member of one of the school sports team for others. That has nothing to do with the question of whether that set of competitions should be segregated by sex - if we divorce it from schooling, it would remain segregated for fairness.
There were lots of electives: photography, architecture, woodshop, auto shop, various fine arts, graphic design, computer programming, etc etc… my school had a pretty long list of electives.
You couldn’t just announce your interest in underwater basket weaving and get a class created, but you also couldn’t just announce your interest in playing polo or rugby or any other sport that didn’t already have a team.
That sounds like a great topic for a thread that’s not about differences between the sexes. It sounds irrelevant here, because even if the competitive teams currently referred to as “high school sports” were instead independent club teams, the leagues would remain sex segregated.

I don’t know. Maybe they’ve quit doing it. When I check my local school district’s website, I don’t see PE, I only see athletics. When I click on athletics, I only see the intramural competitive stuff; which is telling in itself. I know people with children in the schools, I’ll have to try asking.
Athletics is another way of referring to what I’ve been calling “high school sports”. A school’s Athletics program includes all the various sports teams the school fields.
PE isn’t really part of the athletics program. It’s a class taken by students who attend the school, like Math or English or Social Studies. So I wouldn’t expect to see anything about it on the Athletics page.

When I click on athletics, I only see the intramural competitive stuff; which is telling in itself
What do you find “telling” about this?
To me, it’s “telling” about the structure of how schools are run: Varsity, JV, and intermural teams feeding into those are part of the Athletics program, so that’s where you’d see that information.
PE is a class offered by the school, so their course catalog (either the school’s or the district’s) would b where you’d find info about PE.
If there are extracurricular programs taking place at the school after hours, like the very casual (hey, what do you know, coed) tennis or basketball courses I did as a kid, then those are probably being put on by your city, or county, and you’d find that info on their websites. Or there might be a page for after school programs that use the facilities on the school’s page as well.
But there’s nothing surprising about a school’s Athletics program’s web page only talking about teams that are part of the school’s Athletics program…