Hotels require credit cards because without them you get far too many problem guests (drug dealers, partiers, pimps, hookers). Based on my experiences, I wouldn't want to stay in a hotel that didn't require credit cards.
Sorry there seems to be some confusion here. I was complaining that a hotel would not let me pay by card (because they were not declaring the income presumably). "Our machine is broken, we only take cash etc". I escalated it up the chain and the machine miraculously unbroke in that case but it's not the first time I have this kind of experience in a hotel.