Can understand concerns about CCs (and LOL at being a bit trollifying too) but there are pretty good safeguards in the security area, and flexibility too (insofar as PayPal can be used on many sites, which debits your bank account after setup)...
WorldPay and FuturePay can be used on some sites so allowing payment with Debit cards, not CCs....
FuturePay is for regular subscriptions, and either party can cancel, not like a Direct Debit where the company has to stop it from taking money from your account.
Pretty sure there's one company that can issue "once only" numbers, so once that specific number has been used, it won't work again for your name and address. Now that means you can be 100% no fraudster will be able to use it, once you've bought your goods online. Cahoot from memory (though I currently have no CCs - I use debit card and PayPal).
I live alone, so tend not to buy food (but at least one elder sister has done so, for some time, and it means the delivery guy brings the items up the steps to her front door, so less strain on her, when she had had a long day as school head!)
I have bought (or reserved, at local Argos) all sorts of IT and mobile phone gizmos. Really like to compare a few before buying, and generally easier than walking around 3 shops only to need to go back to the first as the other two were "out of stock" (that I really hate, when I've set my mind to get something in particular).
Just today an optical USB mouse arrived, cost me 210p (via Ebay), and it looks like postage from China was about 150p... Loved the fact it has "For Hove or Office use" (as one sister lives in Hove!)
So back to the question - I can quite understand some being worried, or wanting to shop (I love the odd visit to a big shopping centre, like Meadowhall, but as I don't drive and it's 100 miles away, it's that bit more of a treat, esp if it's a "Christmas shopping special" and I'm on a coach with only one other male on board, and he's busy driving!)