I wish. I cringed at the thought of using public restrooms in Asia, because some places still use squat toilets, and in others I'd be lucky if one even flushes. Toilet paper? Don't count on finding a roll, let alone multiple back ups, stored on the roller. And there usually are rollers in the stall. Funny how that happens isn't it?
Maybe it's because people may abscond with a whole stash since disposable napkins, tissue paper, and the like are rare to find in Asian regions to begin with. Maybe it's because a lot of the plumbing systems aren't robust enough to flush any sort of paper, let alone the rough supposedly local toilet paper that probably isn't even engineered to disintegrate in the sewage.
In any case, toilet paper is not necessarily a stocked item. Of course, it depends on where you are and what kind of an establishment you are in. I've been to a five star restaurant in a modern building that has all the normal public restroom furnishings and decor; but it costs you a couple local coins to be given three pieces of toilet paper from the restroom attendant.
There are those adequately built and put the filled toilet paper dispenser at the entrance to the restrooms, vice the stalls, so if you didn't catch it or grab enough on your way in, you will find yourself half squatting with your pants bunched around your knee, wishing you have brought some of your own.
I'm lucky. I've been trained by my own mother from youth to anticipate these instances that are otherwise unexpected by many Western- or primarily North American- travelers. I still avoid squat toilets, but I never travel without a roll of toilet paper. The hotels that provide a miniature roll for the guests? I love them. As stingy as it seems to provide a mini-subset for the guest, those rolls are perfect for me to pack into my suitcase when I check out. Otherwise, I stock up on these. Charmin, for that alone, you have guaranteed my lifetime loyalty.
Men? If only you can appreciate how lucky you have it.