If you pay via a medium that does not return some of the margin to you in the form of rewards or a 'cash/debit' rebate, then functionally you're paying an invisible tax.
This means everyone should be using credit, ideally the highest reward options, which themselves have the highest processing fees, which result in higher prices all around. The creation of higher tiers of rewards and super-premium cards just repeats this cycle, whereby normal cardholders and cash/debit users are now subsidizing high-spend premium card users.
Further, large retailers negotiate significantly preferential rates and lower processing fees for their book of business. This means small and medium sized businesses pay significantly more per transaction for processing, meaning they're less competitive and less pricing pressure is placed on large retailers, which again raises prices for you.
There's also the card issuer side of things, but in short if you're not changing your credit cards regularly, companies will depreciate rewards and benefits over time in previous lines to move you into a higher margin segment of their portfolio.
In short, there's already a divergence, and you're already paying for it in multiple ways.
even with your optimal strategy, you're still paying for it: those points might as well be already spent at the network of vendors you've agreed to sell your purchase history to
it says so in their balance sheets :)
Or put another way: the list price must be reasonably achievable, but charging more for "extras" (eg. a more expensive card with benefits) is always permitted.
The best answer is probably a combination of the two: break out the bullshit costs the customer has to pay so that the consumer can see them, but still give them the upfront cost as early in the transaction as possible.