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.
I agree in your idea but we cannot say that coin that we earned from bitcoin can be save because their is a moment that it is flactuation. Then bitcoin is not a good savings if you really want to save for the emergency convert it i to money and that will be the one for tha savings in case you need it. Their are many ways so that you can use the money from bitcoin.