I wouldn't recommend keeping credit card limits low to only mitigate fraud risk - credit card companies generally will take the hit for unauthorized use, aka stolen information, and send you a new card. So keeping the limit low in an effort to make sure that if your info is stolen they'll only be able to steal $1000 or $2000 isn't really necessary, and only affects your ability to use credit and have a better credit score (because your % of utilization of your overall credit limit goes into your FICO).

Instead, review your purchases monthly and inform the card company of charges you didn't make as soon as you see them.

DEBIT cards are a different story. They're a direct link to your bank account funds and there's no intermediary that is willing to take a hit, it's your bank vs you, so if your debit card info (and pin) are exposed you're much more vulnerable. So I wouldn't recommend EVER using debit these days, there's zero reason to, but if you have to then your advice in your OP is more appropriate.