Interjecting for a second.
When looking at whether women are excluded from these environments, there is a tendency to look at things based on rules ("There is no rule keeping women from participating in Smash; there is no law preventing women from becoming engineers").
Most cases in society no longer have lawful structures that keep people from participating in what they choose (outside of financial barriers, but this is unlikely to be solved). Instead, there are often times social structures that can dissuade people who may benefit from participation. It can be as wide ranging from active dissuasion ( telling an outsider to GTFO) to simply not seeing someone similar to yourself .For example, if there are no black students at the school you want to go, even if the school is a perfect fit, you may end up having doubts on whether you belong, whether or not anyone has actually told you you didn't belong.
This is why many social structures actively create programs to ensure that minority populations are given attention-these programs more often then not work in retaining minorities who have taken the plunge and encourage others to join these institutions.
Tying it back to Smash, we can see a clear disparity in the number of women who participate in the competitive scene (this isn't removed from competitive gaming in general though). Is this a problem though? We've heard from community members like Milktea that the community isn't always the best towards women. We're also not that far removed from the Alex Strife fiasco. We could certainly do better in encouraging more participation from females. By doing so, we could allow for a fostering of talent that otherwise wouldn't have had the space to do this.
While a female-only tournaments may irk some, I think it could work in providing a space for female players to engage with each other. People like being in places where they have others like themselves involved, and having a tournament like that could help in providing a comfortable (in comfortable, not in a "men are creepers" way, but in a "other girls may be fun to play with" way) space for players to play.
I don't think the problem has anything to do with sexism at all. I think it has to do with the mentality of female smashers themselves. Every time I see a girl at a smashfest or tournament, they kinda just sit in the corner not participating or play a few games, then say that they aren't that good and stop playing. The issue is that they give up before they get their foot in the door, which will mean that they will always be bad and therefore never taken seriously. Another issue is the "I don't want to go because it's gonna be a sasuagefest and I don't want to be the only girl there." mentality. If 10+ plus girls believe the same thing for the same event, then you can see the fallacy with that thinking.
This is an example of what I mean. They likely don't feel comfortable or welcome- it isn't anyone's fault for this. Even if they enjoy the activity, they might feel like they don't fit in. It's like if someone goes to a party where they might feel out of place; no one's causing them to feel alone (though someone might), but simply because of the makeup of the room, they might leave before they could gain something of value from the party. If we can avoid this happening, this is a good thing.
It implies that women = JV, which is the root of most sexism in society.
Like in the chess example, women's events should never be a counterpart to the main event. In your examples, there is men's Olympic sports and women's Olympic sports; the NBA and the WNBA. We should have an Open event and a women's event, with real incentives to be in the main event (larger prize pools, better competition, etc.). Women's events should not be where women cap their play-they should (and probably will) be encouraged to join the full competition.
I think the more important question is "Does Smash have the financial backing to run such an event?" On a grassroots level, not really sure, but I would likely lean towards no given the shoestring budgets most tournaments are run on.