Comment by toast0

I don't think the intent is really to break up Visa and Mastercard, but to allow merchants to accurately pass through their variable costs.

If merchant fees are < 1% if I use debit and ~ 4% if I use a rewards card, but merchant rules (set by the networks and enforced by the acquiring banks) say they can't accept amex and surcharge rewards cards but not debit cards, they can't reduce their costs by pushing me towards debit cards or non-rewards cards.

There's some other things they're challenging that could allow for more competition.

Removing the 'No-Bypass Rules' could allow for lower cost clearing if the acquiring bank is the same as the issuing bank and the potential for lower cost clearing when the the acquiring and issuing banks have a clearing relationship outside of the major networks.

Removing the 'No-Competing-Marks Rules' could allow for a card to be Visa + some upstart lower cost network; if the merchant supports it, great, if not, they can still process payment through Visa. I think US law requires ATM cards to be usable through at least two distinct networks, and there's at least some diversity in ATM networks as a result.