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The major card networks (not sure if that's the right term, issuer isn't either), all entered the business around the same time, and all from a position of banking or at least providing credit (Discover was created by Sears).

Of the companies you mentioned, only Paypal could really do this, and in fact, they did have some in-store options available, although they're apparently being shut down. It's really a marketplace problem though -- you have to have enough consumers so that it's useful to businesses, and you have to have enough businesses that it's useful to consumers. And you have to have enough clout that the rest of the banking industry won't refuse to deal with you.