I think it was felt that A & B should be free to make whatever deal they like with each other, and likewise for B & C. But should A & B be free to make a deal that constrains B & C? It was felt the lesser of evils to outlaw A & B from constraining the freedom of B & C.

From memory, much of the motivation was the near-duopoloy operated by the credit card companies. In practice, merchants were not really "free to make whatever deal they like with the credit card companies". You had to offer the same deal to cash-payers. This meant that more consumers would use credit cards (why pay by cash if you can get a period of free credit) - and credit card companies would have no incentive to offer a competitive service. Over time they would take more and more margin from merchants and/or prices would increase.

Anyway, whether flawed thinking or not, it was felt against consumer interests for them not to be able to get a better price for paying another way (eg cash).

EU law (Article 81 of the EC Treaty) has also prohibited such arrangements except in special circumstances. Its regarded as a form of price fixing. In general suppliers are not permitted to fix (in anyway) the selling price given by their customers as a condition of supply.