Something often not spoken about (as the discussion often focuses on privacy and "power") is the price.
As someone who uses card for most payments (maybe paying in cash a couple of times a year), cash is expensive to use. It requires time out of my routine to take the cash out, unless I can take out an exact amount there I'm then left with change, and then because I don't want the change I normally spend it on things I don't need. If cash in another currency that's very expensive as I have to pay to convert the small amount. On the other hand cards are effectively free to me, even paying in other currencies. I travel a lot and never use local cash.
However, for many people, the reverse is true. If your cash flow is primary in actual cash, then paying into an account can be annoying or even cost money, current accounts without sufficient funds in them often charge a fee (in the UK current accounts, checking accounts?, are typically "free"), some users can't even hold a real bank account and are forced to use pseudo-bank-accounts based on prepaid cards with exorbitant fees, and cash could be argued to subsidise card fees (which are rare in the UK).
I hope that for the foreseeable future both options are accepted at the majority of places. I'm never going to take cash out for a truly discretionary purchase so only accepting cash limits the market, and some people are rarely going to have a card they can use at card-only merchants.