Back when I was doing payment code, I built several sites which didn't prompt for the card type, since (a) the first digit identifies the association [1] and (b) the processor doesn't usually care anyway, i.e., you don't need to submit a card type value along with the rest of the transaction data. Most of the clients for whom I built these sites complained about the lack of a dropdown, and were not terribly receptive to my explanations on points (a) and (b) above; their line of thinking on the matter was that people expect to see a card type dropdown, and will complain in its absence. I rather doubt that's true, but I have also never considered it really my place to argue too strenuously against a client who refuses to let me save them money, so more often not I ended up adding the dropdown anyway.
During my time working on websites for a retail company the imagery of the credit cards accepted were considered important. They would even be on pages that just mentioned taking payments before you get to the actual input page.
One reasoning is that it is a sort of reassurance, much like the stickers you see on doors of retail locations that show which cards they accept. It's a reassurance in the idea that if you're deciding if you want to make the purchase or not, that the site will have no problems in accepting the payment option you would like to use. Plus, in a strange sort of way, it implies the site is a valid on-the-level company because surely a credit card company would come down hard on a scam site for using their copyrighted visual identity.
There's not much valid reasons other than it's a visual thing for customers. Although I always suggested using the method of displaying the type of card after starting the number, that goes against the reassurance thing. If a customer has two different branded credit cards, they know up front if one or both will be accepted. Otherwise they have to start typing to find out, which is work for the customer. You always want it to be easy for the customer to spend money, no second guessing.
All of what you say is true, but I was referring to a dropdown or radio button set for choice of card type, and not the card type images themselves, which I always included unless the client preferred otherwise -- something I don't remember ever happening, now I think back.
- You have a row of credit card icons. By default they are in full color.
- These icons react like buttons (hover shows clickability) and act like radio buttons if clicked -- all the others gray out.
- When a user starts typing a credit card number, it selects the appropriate icon if not already selected (graying out the others).
Because they aren't radio buttons (or a dropdown), it doesn't force people through the step, but because they can act like radio buttons (providing only visual feedback), they don't confuse anybody who thought they were supposed to be there.
The forms I've used that feel the most natural do something like this.
I may be talking out of my ass, but if I recall correctly back when I had a merchant account I may have been required to add that drop-down even if it was meaningless.
[1] 3 = AmEx; 4 = Visa; 5 = Mastercard; 6 = Discover.