I don't think I've ever heard of a credit card processor that didn't process funds through a merchant account. I don't believe those exist.
I also don't think that a voided check is exactly a burdensome, unrealistic request, but that's just one business owner's opinion. ;o)
From what I've seen, credit card payments are commonly available by the close of the following day, and then it's up to your bank to post the funds to your account. So, two days. How does that timeline compare to taking a paper check to your brick-and-mortar bank and waiting for it to clear?
Chargebacks are the nature of the beast when dealing with credit cards-- it's all tied into consumer protection. You might read up on Google Checkout
-- they've got a good reputation for being pretty strict on protecting their merchants from fraudulent chargebacks. If you're selling physical items through the mail, requiring signatures and sending everything with tracking is very important in giving yourself protection against chargebacks of the "I've never received it" sort. Maxmind
is also recommended by some to help cut down on fraud, if your business is of the "sell things on Amazon or eBay" nature. In Food & Beverage, where people just abandon their cards and tabs and report the cards as lost or stolen, it's good to hang on to their driver's license instead, and maybe mix it up with a little pay-as-you-go. If you've got a vice-based business where you're worried about your patrons waking up the next morning and feeling remorseful, you might just switch to cash. :o)