It's all part of 'their' plan to convert us to a cashless society. It's much easier to control, monitor, and manipulate someone when you can track every purchase they make (and every source of income), and where they make it, as well as having the ability to completely disable someone with the push of a button by cutting off their accounts.
Next comes the mandatory microchip. And of course it's always for our own good, our own convenience, and our own safety. They'll make you do things, then make you think it was your idea! 
.....or I could just be a kook.
And no, I would not shop somewhere that doesn't accept cash. Even if I wasn't planning to use cash. It's simply un-American.
I heard this debated on NPR on my way into work a few days ago and nearly called in (Airtalk on KPCC I think it was).
The problem with this is the banking industry isn't setup this way; at least on a study I saw on this by the FDIC in 2015 7% of the population was flatly unbanked, and 19.9% were underbanked... though according to their definition that includes a checking or savings account and if you can get one of those, you can get a debit or prepaid card.
The 7% that doesn't have it though, you can't just walk into any bank and get a checking account these days if things like your Chexsystems is out of whack; it may not be possible for these to even get most prepaid cards as a result.
There'd have to be some institution that you could deposit cash at and get a prepaid card without any reservations, accessible to anyone and everyone with a pulse, and that is not the modern bank though I suppose they could be encouraged to do that.
It's a massive undertaking to try to address this, we may get to mostly cashless in what I'd liberally call somewhat affluent America (the ones regularly eating at restaurants that Visa is targetting... you absolutely don't have to eat at restaurants and it is generally more expensive in dollar value therefore it is a luxury looked at in this manner) but what I don't want to see is a stratification of American economy based on whether you can get a prepaid card or not, and if refused service because you cannot pay in the manner expected which is going to disproportionally hit a specific population group of the American consumer base unless I very much miss my guess, and that is going to get the ACLU among others up in arms and I'd be supporting them with absolutely no reservations on this one.
To answer the question though, I probably wouldn't even notice if a store didn't take cash whereas I do notice if it doesn't take credit cards.... as soon as I got my first credit card (10/2011) I've paid anything and everything I could with a credit card.
