... For how long should people understand the importance to have bitcoins for emergencies such as this one?
Okay let's assume the lady has bitcoins on her non-custodial wallet but she still needed to sell it for fiat because the hospital doesn't accept BTC. What if she tried to trade it on a centralized exchange and the platform suddenly froze her account for some reason? That's still going to be a problem. How about P2P platforms? A lot of them requires bank accounts for trades so the same issue.
It's not really bitcoin's problem but the point here is that there is always a risk as long as people continue to use centralized platforms.
Even when we use a DEX, are your Bitcoin sales not going to be paid into your Bank account? As far as I know, for now, the DEX I have used also pays directly to your Bank account and we are back to the same problem except you know someone that is willing to pay you by hand directly.