I do not agree that it's being "prepared", it is being paranoid after a point. If you really want to, 10% of your portfolio could be USDT, and that way you could have some emergency fund.
But, I believe AT LEAST 10x of your emergency fund should be in BTCitcoin.
Emergency might come or not, and it you use part of your emergency funds, you should refill it as soon as possible. Emergency funds should be in our local fiat currency for eash accessibility or you can leave it in USD, if the value of your local currency is a problem.
You're right emergency funds and back up funds should be in our local fiat currency, just as most people have been preaching about putting all our Money into Bitcoin. i know they might be doing this because of inflation which is also a good reason, but putting all our Money into Bitcoin is not a wise idea because when there is emergency definitely you will have to withdraw some portion of the Money regardless to the market condition this is why I feel that our emergency fund and back up funds should be save in fiat currency to avoid messing up with our bitcoin investment.