Considering bitcoin investment as emergency money doesn't seem a bright idea because this will mean that once you need the money you should sell it a market value and sometimes it could be below your entry point.
The exit strategy is a long time movement because you must wait for the right price to convert your money into fiat so you won't be able to have access to your funds right away.
Emergency money should be in fiat.
We have an app here in the Philippines that can immediately convert your btc's into withrawable currency. All though the price would be much lower.
And I agree with you, taking btc's as emergency money is not a good idea unless you there's a nearest public services/business establishment that accepts bitcoin as payment.