Some but MasterCard and VISA's contracts both require the merchants to accept all of their cards, or none. Their market share makes it less practical to decline all MasterCards or all VISA cards than to decline American Express or Discover. Allowing merchants to reflect transaction cost differentials should create greater competition. Having some is good, having more will be better.
Many education institutions do decline Visa and only accept MC/AMEX/Discover.
I have also seen merchants with PayPass terminals that only accepts MasterCard.
I have no problem with merchants that only accept Visa or MC or AMEX, or debit only for that matter, because they clearly display the network's decal on their door so I know before I enter the store instead of finding out
after I finish a meal and ready to pay.
It creates massive confusion for consumers if merchants are allowed to accept some but not all Visa / MC Credit Cards.
As if it's not complex enough already? "Yes you can use this World MasterCard but not that World Elite MasterCard?"