This sends the message that people with money can do whatever they want, environment be dammed. We need to simply ban things that are terrible for future generations, not continue to allow people with money to do it.
The cup is a product that is currently perceived as gratis / of zero value. Charging for it is intended as a disincentive. In the case of plastic bags (here) it largely worked as such (with prices as low as 10c per bag!) and paved the way for a ban. Though the parallel effect of more resource-intensive bags / cups entering the market / being treated as single use is always a consideration.
But to your broader point, for sure .. bring on a ban.
I don't think such a stigma exists? As a regular coffee drinker, I've never heard anyone comment upon anothers cup choice or even raise an eyebrow.
At some point using non-reusable cups and similar things should be akin to smoking in a crowd. And if smoking among other people isn't frowned upon wherever you live, you should start with that first =)
Yes, rich people can do what they want, but at least it doesn't hurt the rest of the people.
Doing so uses up more time and resources that could have been put to better use had the transaction never occurred in the first place.