I grew up in a household where my mother's san pro was always on view besides the loo, whether actively in use or not, and mine is now in my house (it's convenient there.) I also don't go to any particular effort to hide sanpro in the walk from my desk to the loos at work - it's usually just in my hand, as I keep it in my drawer.
But I don't want to do freebleeding on the heavy days. It's fine when the flow is light, but the rest of the time, I have to do my laundry, and that's enough of a faff without it being blood-stained. (I fully appreciate chucking stuff in an automatic machine is nothing like the faff it was for my grandmother and - well, earlier generations, for the staff.) We clean up bodily fluids, and menstrual blood isn't any different - it's mostly about hygiene.
I would suggest the reason things changed through the 19th century is because that there were loads of changes in public health and individual health. Water supplies improved, people got access to water closets, towns got public sewers, there were public wash houses. There was better understanding of how diseases and so on spread. There was more public interest in how people's lives were lived. Also, skirts used to be pretty much floor-length - it would mostly have only been petticoats which were bled on, and in the 20th century, skirt lengths start moving upwards, exposing ankles, calves and knees, so freebleeding just wouldn't have been as discreet. And houses these days are often carpeted, not bare floor strewn with straw, and you can't muck out a carpet in the same way. I would think there were a whole load of factors that feed into it, and it just becomes less common.
But while I wouldn't go as far as freebleeding, I don't see why menstruation has to be a secret. If my colleague can say, "I'm off to the loo, had a big curry last night," (which frankly is TMI,) then I don't see it's any worse to say, "I'm just going to the loo before I start leaking." Though to be honest, I wouldn't think I'd mention it at all - if I do, it's likely to be, "I just need to pop to the loo before the meeting starts," without going into any detail about exactly why (not least because occasionally it's just that I need 5 minutes away from my phone!)