The 16-digit system is ridiculous. If you're going to use your card online, or in restaurants, etc. your card number is quasi-public.
Two of my cards have an option which sends email and/or SMS and/or app-notifications upon every transaction, accepted or denied.
I caught a bogus attempted charge last month - this saved a lot of exposure & aggravation. It also informed me last week when my personal activity caused my card to be suspended ( several international charges, different countries in the same hour). CapitalOne, Discover, & Chase offer this, and I assume some other competitors do so as well.