People have been dying for even longer than credit cards have been around, so we should expect that this ubiquitous phenomenon has been accounted for in the credit industry's business model.
When someone dies, their debts don't disappear - the debts are paid from the assets owned by the decedent before heirs/beneficiaries are allowed to inherit.
Credit card balances can be negotiated down after death - but that happens pretty frequently with living people, too, through bankruptcy or otherwise.
Lenders don't expect that every debt will be repaid in full - it's part of the business model.
At least, this is how it is in the UK.
I'm less worried about people dying with debt than I am with young people having to pay huge debts off, and having to save for old age, at the same time.
What happens then?
Why start worrying about this now?
You know what would be a huge PITA and a lot of work? A death app. Even if its nothing but a flowchart and checklist and the best customer support on earth. Presumably everyone who owns a smartphone will eventually have a friend or relative die. Plus you could coordinate marketing with the funeral racket. Death is a big (highly corrupt) business and a startup could collect a slice of that pie.
For example, for gods sakes whatever you do, don't go and stiff the IRS (oh the pun) in favor of paying off Citibank credit cards, especially after probate begins. There's a whole complicated legal hierarchy and set of definitions of who's responsible for what, WRT probate. If you basically appoint yourself probate judge and probate executor all on your own, as a loose cannon, you have no idea how big of a legal pile of bricks will fall on your head even if you're "just trying to help out with the paperwork".
Or another example, unless you're the named or appointed executor, for gods sake never take a phone call from a debt collector, fraudulent or possibly even legit, unless you're a cosigner or joint owner and even then talk to a lawyer first. Crooks will be ringing your phone off the hook if its known the deceased had a positive net worth. Its fairly likely you'll have both the mortgage company and two or three crooks falsely representing themselves as the mortgage company all trying to get money and/or identity theft information. Repeat for all possible services, including public utilities. Shut off the phone ringer and have a close-ish family member with a clear head take all incoming social (and criminal) calls.
If you use the deceased's credit card to pay for the funeral, legally or not, you can expect the debt collectors to go after you personally for the full balance on the card, legal or not. Usually it only costs a couple thousand in legal fees to fix this if you make that mistake. How to properly and legally pay for a funeral is an excellent question and probably varies a little from state to state.
Even just a checklist could be valuable. Did someone contact the cellphone company both on the phone and in writing as most require, and if so, who, and when? During probate they're going to be discussing this so not losing the data might be a good idea. Ditto the water utility, the water softener salt delivery service, the electric company, etc etc.
Those are just some anecdotal stories I've heard over the years that could get rolled up into some kind of advice app or service or whatever. I'm sure there are many more. Usually it doesn't turn out that bad, of course. But it can be very bad, yes.
I'm old enough to have seen enough ancestors die (more than just immediate family of course) and there's a large business oriented around making sure middle class people never inherit anything. Its hardly a new problem. All of someone's net worth is supposed to go to the medical industrial complex, or a couple other places. You can safely assume that whatever boomer generation net worth is, approximately zero is going to gen-x other than the highest net worth of the 1%. Same thing happened with the WWII generation and presumably every generation before them.