I think the poll question is missing an important piece. There are many games on itchio that do have a female protag - and sometimes it's the only option. However a female MC alone does not define the otome genre. What matters is the number of male love interests as well.
I've come across games that have a female MC, but the cast is split evenly between male and female love interests, which means it has a lot of GL elements. I wouldn't call those "otome" either.
Honestly, I find it pretty weird that nobody seems to check or supervise how the tag is being used.
It's actually par for the course. It's annoying yes but that's how those stores operate. We know otome well because we're part of the fandom, but you really can't expect the companies to assign an employee to only check tags and supervise them for thousands of games per day. Nobody has that kind of knowledge across every single game genre, and it's a waste of human resources.
To compromise, Steam allows user to flag wrong tags or assign their own tags (if it's popular enough, it'll get officially attached to the game's tag list). This means the power to curate tags is in the users' hands, but it also leads to abuse like trolls putting the wrong tags on purpose. I honestly like the idea behind the system, but terrible humans always prove that we can't have nice things.
On the other hand itch.io is very "pro-developer." What this means is the developers have the final say in defining their games. If they attach "otome" to their work, well you gotta shut up and accept it, even if it's wrong. The community is "woke" in all the wrong ways too. If you try to speak up (even if politely) about their game misusing the "otome" tag, you'll get downvoted to hell by the fans and called gatekeeping, homophobic and whatever other insults they could come up with at that time. The developers also can just turn off all comments and discussions, so good luck finding any way to voice your opinion

A proper review system? Non-existent on that store too.
Instead, I decided to suggest a new tag description that explicitly states that the protagonist has to be female.
I'm not sure I understand you correctly, but there's already a "female protagonist" tag on itch.io.
The issue isn't the tags' existence, the point is DIFFERENT TAGS ALREADY EXIST BUT DEVELOPERS REFUSE TO USE THEM CORRECTLY (I'm not yelling btw, this is for emphasis)
Exhibit A: the Amare tag. This term was coined by the English visual novel community themselves, for the exact use cases that involve every-gender x every-other-gender type of romance games. But so what? Developers would rather tag every dating sim on Earth as "otome" and get the extra marketing, rather than use "amare". It's useless.
The English community will continue to be "woke" and want everything to be made for everyone. Otherwise they will cry about it and feel left out. Misusing tags is treated as some sort of "evolution of the language" and applauded by the community. However, the funny thing is, only "otome" has to evolve to include every gender identity.
Nobody dares ask the same of "eroge" or "yuri" where the male audience reigns supreme. But if you tell them women need our own space for our hobbies, they'll cry about how oppressed they are as LGBT people. Yeah baby because women have been soooo unoppressed throughout history, and even now, amirite?
Am I missing something, or has the definition become so broad that it barely means anything anymore?
You are not missing anything. Anyone who actually cares about "otome" and have functioning brain cells will respect and understand the genre for what it is. It has not evolved to become broad. It's always been focused on the story and hetero romance between female protagonist x male love interests.
But the English community already opened the floodgates, frankly we don't gatekeep hard enough so now that it's come to this point, I don't think we can expect any improvements.
Even on the so-called "IndieOtome" reddit you have people asking funny things. Like WLW dating sims or dating sims that have male mc (???)
And of course mods do nothing, the members do nothing. Somehow "otome" is being treated as the de facto term for just...dating sims and members of the otome community are expected to give recommendations for anything
Meanwhile devs will continue to tag their 123456789 early access alpha wip demo whatever they want and the fans will coddle them while waiting 365 days for an update (unironically that's the general status of most games I've seen on itch these days)