PCI is surprisingly easy (and anyone can look it up at https://www.pcisecuritystandards.org/security_standards/docu...). It's basically all about "data at rest," covering what can be stored, how it must be stored, and how it should be stored. If a merchant can't meet the requirements, then they are required to demonstrate "compensating controls" which can literally be "we have a project in place to fix this before the audit a year from now."
"Data at rest" involves (in this case) credit card information stored on "disk" (SSD, etc.) for more than a short period of time. This generally excludes virtual memory, some queueing software, etc. If it touches the disk for ten seconds but is then wiped, you're compliant.
Then there are a list of "musts". You must have firewalls protecting the internal network (and review the rulesets), documentation on any connectivity to cardholder data, dataflow diagrams, only allow essential traffic in the card info environment, wall off wireless access, have an IPS, change all vendor defaults on any devices that could possibly screw you, minimize server responsibility (so don't run your smtp relay on the machine that also encrypts your card info), rotate encryption keys every x days, don't store CID/CVV/track 2/full mag-tape data from the card, scan your systems for changes/compromise/unauthorized access, maintain nonreputable audit trails, etc.
PCI is ratcheting down the requirements so that there is less room for interpretation. Previously, just using Oracle's obfuscation toolkit would be enough. This would protect you (more or less) if someone had access to your block device in raw mode or your data files in what-the-hell-is-your-dba-thinking mode, but an Edward Snowden could log in and SELECT all of your card info.
I agree that a cc user should not have to care about any of this, but people responsible for protecting your money are not so responsible.
(And most people are fairly aware of the fact that card numbers are sensitive information; the newish thing here is a large retailer failing so spectacularly)
The key piece to keep in mind is that the info on that little piece of plastic is never "safe".
If I were warning my mother, I'd just follow your hypothetical above. Of course, if the outcomes of these data breaches start including other identity theft, such as the "$50,000 twitter name"[1] hijack, more realistic phishing attacks, etc., then things are going to get interesting.
[1] Which is of course silly since the TOS specify that they are not to be sold.
They are not easy nor simple AND you can't use your credit card while they mail you a new one
So yeah, as someone who have had their CC misused, it's a pain in the behind
If you use a debit card, go to your bank and have them turn off the "feature" that lets you overdraft (and get charged a $35.00 fee each time). Set up a separate account (one that doesn't have a debit card), to use for all your bill payments, so at least that doesn't get behind if your main account is cleaned out.
There's numerous disadvantages, the main one is that that you generally have less protections against fraud, and even if you do, you may have to wait for the transactions to post before your bank can reverse them.
There's no upside to using a debit card; get multiple credit cards and pay them off every month. There's also various upsides including more air miles/hotel points, cash back, travel insurance, etc.
Better yet, have them issue you a new card that is only an ATM card and cannot be used without furnishing the PIN. That's what I did back in the 90s when "check cards"† were first introduced. I phoned the bank and asked if the Visa logo meant the card be used without a PIN. When they said yes, I told them to close the account. Instead, they said not to worry and sent me an ATM-only card in the next day's mail.
I use my ATM card for banking only. Everything else goes on my AX (or DS or, in extremis, MC or VI).
†https://www.usbank.com/checking/us-bank-visa-check-card-debi...
I understand the reasons why cash can be inconvenient, but I doubt it it less hassle then dealing with a bank/CC company over fraudulent charges, associated overdraft fees, and all the crap.
Now eCommerce transactions over the web is a different story.
It's also recommended to have a Visa and a Mastercard (but that's for an unrelated reason that a small number of merchants take one and not the other - and usually it happens at the worst possible place, like a taxi).
I don't know much about PCI compliance, but I don't get the idea that it is something I should have to worry about as a user of a credit card.