This conversation is great.
Do want to take this moment to remind every menstruating person here ...
menstrual cups are the most frugal, eco-friendly, comfortable, and least distracting form of period product.
Except for the accidental blood bath in the public rest room stall. I found that very distracting.
The actual changing is a lot more distracting, but happens a little less often and I don't have to carry around as much stuff.
I assume you fumbled? I have done that, but luckily not in public.
Some say it is great for camping. I cannot begin to imagine how that works.
It's not that bad. I took mine on a two week trip to Tanzania so plunged deep into the camping/poor sanitation/limited water life with it after a few months of use. I took my water bottle into the stall, plus wet paper towels if they were available, or wet wipes if they weren't. Sanitize hands, remove, dump, rinse with water bottle, dry with TP, reinsert, wipe hands with paper towel/wet wipe. I can wear my cup all day except for on the very heaviest day of my cycle versus changing tampons every 4-6 hours, so I think it's worth the minor hassle.
As for water usage making it less sustainable...I guess it depends where you live. Here in the Midwest where composting & recycling sucks and water is abundant, I think it's clearly the better choice. Maybe if there are compostable tampons (I've never researched this) that makes more sense in a water constrained area. But it's definitely the most frugal option, I haven't spend a dime after my $24 purchase a year ago now--would have gone through 3-4 boxes each of tampons & liners by now.
ETA: I guess backpacking would be different but I imagine you'd just dig a hole to empty into. Still seems better than packing out used disposable supplies to me.