I imagine this line is annoying people. That you aren't bothered isn't the issue if others are. That you don't see the issue with a delay, or a background check, says more about your one-size-fits-all view than the complexity/simplicity of the problem. Personally I never have menstrual issues so I don't understand what all the fuss is about.
I come from country people, where even today going to the city is an event. And it's almost a holiday to go to "the big city". So a purchase you might be able to go to walk to the store to start a waiting period for might be between two months-apart trips for my family and much more inconvenient.
You also sound like you live in the city so your needs for protection are a lot different than in the country. In the city a pistol with frangible ammo, or a shotgun at home, are the max you'd need. In the country my driveway was 1.5km so different solutions are needed. What's a scary black gun in the city, when in the country, is a way to both keep coyotes from livestock at great distance and defend yourself from people if needed. Being 500m+ from a problem means you need more bullets (larger magazine) than being at 3' from the bad guy in the city, etc.
They're different worlds with different problems.
Look at Canada where the issue recently become polarized but not across party lines. Some nutcase in a surplus police car with a replica uniform drove around a small community gunning people down while the police holed up in the city for safety. He preyed on country people many kilometers from anyone else, with a rifle he'd smuggled up from the USA. Now the city people want to ban scary guns despite that a ban wouldn't have interfered with this shooter, but people from the country want to buy exactly the same gun he used because it's the best-in-class for home defense in those same scenarios.