The tragedy of this is how such stupidity polarises things so much. Take an example I consider valid: using "she" sometimes for a hypothetical person rather than always "he". It doesn't do any harm, remains grammatically correct and doesn't invent weird and contorted terms like "fireperson". When I write documentation and I need to do this, I'll alternate from time to time, just keeping it consistent within any given example. (I.e. if "he" has to connect the monitor to the computer then "he" is the one who then has to turn it on. But later in another example "she" might replace the hard drive). It's a mild rebalancing that normalises the use of the female gender in language and doesn't offend anyone other than hardcore anti-PC brigade (Scorza incoming).
I just use 'they'. It's already in common usage and it's already ungendered and it's already consistent. It simply works. Some people will object to the use of the same word for singular and plural, but it's been used that way for centuries and people manage. English is full of things that aren't always perfectly clear.
Your approach not only retains gender in language but hugely increases the focus on it because it requires keeping count of every time a gendered word is used. It will also offend some people (and not just the "hardcore anti-PC brigade") because they will perceive some imbalance even if you do keep perfect score.
But then instead of something small and reasonable like that, you get a barrage of things like how "waitress" must be replaced with the frankly derogatory (imo) term "server", that housewife should be "consumer" which is dehumanising as **** and all that other long list of nonsense.
I find "server" less annoying because it's more accurate. I use the word "servant" for myself, because that's my job. Euphemisms intended to give a false impression of the job (without actually changing the job) grate on me. They're like spelling out "w..a..l..k" so a dog won't recognise the word 'walk' and that's insulting to a person. I'm employed as a low grade servant with low status and low pay. A flunkey.
I'd prefer to get rid of the word "housewife" myself, although I'm not sure what I'd replace it with. It's far too gendered for me and the masculine version ("housewere") isn't a word I've ever seen used so the genderisation is pretty much total.
So the net result is the whole thing becomes massively polarised by people quite reasonably sick to the back teeth of this crap and defensive proponents who regard everyone criticising them as misogynists or dupes (if female). And the handful of quite reasonable things like using "she" in examples sometimes or "they" for a gender-uncertain singular pronoun when appropriate become hills on which people must die.
Idiocy.
And all too common. There are only ever two mutually exclusive and opposing sides and everyone must pick one and fight the other one!
For a species that's justifiably proud of our ability to understand complexity, we're very prone to massive over-simplification into opposing pairs.