Visa and Mastercard have invested so I wonder how they might weigh in on the project. Also, the Libra-coin should also have a transaction cost associated but I would expect/presume it stands an order of magnitude lower than 3-4%
Visa/Mastercard consider crypto an existential threat - the value add that they have in terms of consumer protection, middleman conflict resolution, and fraud prevention does not add up to that 2-4% level of value, and they admit that. Trust and the network effect keep them in play for now.
Crypto transactions however, have not lived up to the "hype" of being truly cheap thus far. Visa/MC are positioning themselves such that the value they bring is not something that crypto can provide. We'll see where that ends up - I'd expect Visa/MC stock to move a bit if the transaction fees for Libra end up being sub-$.05.
It isn't clear to me that you wouldn't still have payment processors anyway.
In the UK right now I can send money to your account nearly instantly, and for free. I wouldn't want to purchase anything like that though, I'd want to use some kind of card, why would Libra be any different?
