Talk about off topic wandering...
US experiences - I'm not as rural as I used to be when I lived in the West. Around here, most gas stations have open toilets these days. For a usually cleaner experience if I require some sit down time I look for a pharmacy. Both CVS and Walgreens have public bathrooms, usually in the back of the store. Mostly cleaner than average, but not aways.
Walmarts also nearly always have a cleaner bathroom in the back of the store than the one in front. Best Buy is another location with clean bathrooms, usually. Dollar Tree stores have bathrooms usually available to the public, as do Aldi, Kroger and other grocery type stores.
If I'm out in the rural areas and have concealment, I have no issues with a pee in the woods or just by the side of the road if conditions and apparent traffic allow.
When I do multi day rides I do carry a plastic trowel. I always carry a partial roll of TP, because you just never know when it will come in handy.
In Egypt, you just walked off into the desert a bit and took care of things.
In India, right by the side of the road, against a pillar, etc. In '12 there wasn't a single porta potty in the entire country, near as I could tell. Hopefully it's improved by now.
Peru was better, but still had remnants of the distasteful India custom of no TP in the bathroom and some 'attendant' willing to sell you a few sheets and begging for money because he 'cleaned' the public restroom you were using. I ALWAYS carry TP in a pant leg cargo pocket when traveling internationally, even if it's the EU.