So, some new central authority issues cards with their own account numbers (formatted the same way as current credit cards), which the central authority links to a bitcoin address and does the transactions. Yes, that would be nice, but, as you say, there's no such trusted giant to be the processing authority. Plus that centralizes bitcoins, which negates one of its benefits (decentralization). Plus the central authority would probably need to take fees out for its own profit from every transaction, which would put it back to exactly like the current credit card company systems, which I don't think is where bitcoin wants to go (it's a new currency, set to correct mistakes of existing systems, not repeat them).
Can you explain to me why decentralization would be necessary for a service like this?
The fees are not for profit. They are the minimum required to maintain the integrity of the service being offered at no cost to users. Merchant transaction fees are hardly the issue here, it's the monopolies credit card companies have over all digital transactions be they at POS or online.
Decentralization is not necessary for the process you've described. Quite the opposite, actually; it needs centralization to work, focused on one or few central banking authorities. The point I was trying to make regarding decentralization is that Bitcoin is based on principles of decentralization, so solutions that move it toward centralization go counter to that fundamental belief, and probably wouldn't be as readily adopted. Yes, the fees by a central banking authority
could be just enough to break even, but if there's only one bitcoin central processor, they're not really competing with the standard credit card processors, so is still pretty close to a monopoly, and could charge whatever they want.