I'm not in the "not my problem" camp, as some people apparently are, but I get cash-back on my credit card - I deliberately choose a credit card based on that, and deliberately choose to pay by credit card due to that - and so we're all better off with my tipping on my credit card rather than me tipping with cash subtracting my cash-back consideration out of what I'd have tipped otherwise. In a nutshell, servers are having the gratuity subsidized by their employers, who pay the fee associated with my using my credit card, without that necessarily having to come out of the tip.
Beyond that, I carry about $20 on me. It's the same $20 in my wallet right now that has been there for a month or two. Probably more, actually. I get to an ATM perhaps four times a year, max. I pay in cash - basically never. Cash is not the way I want to do business. If servers really want another way for me to compensate them, then they need to provide me an option as convenient and as otherwise attractive as credit cards: It isn't a matter of me saying that it is "not my problem", as I mentioned before, but rather a rejection of the server telling me that their concerns about me tipping by credit card is not their problem - it actually is their problem, and therefore their imperative to offer an alternative more attractive than credit cards.