In regards to your suggestion that the extra BTC could serve as an emergency fund is not completely off point, since whenever anything is extra there are options with it - yet still it does not tend to be good practices to have your emergency fund denominated in something other than your own local currency... which truly having BTC as part of your emergency fund could lead to selling some of them at price points that are not very convenient.
that is true, it is good to have our emergency fund in fiat instead of having it bitcoin. you know sometimes people might be having issues of emergency and we just need the emergency fund to sort some things out but some factors may deprive us from get it immediately as expected or not having it exactly as expected, such like:
1. Delay of transactions in mempool, someone may be trying to sell his coin in return of emergency fund during the period mempool is congested and transaction may delay just like the having period, when people find it difficult to trade there coin. some transaction where pending for a week or more with a higher TRX fee.
2. during the time of selling of BTC for emergency it could be that maybe your 1 btc at the rate of $70k may have fallen to $60 losing a huge amount of $10k.
3. Dollar/fiat may have dropped. for example you may have the opportunity to have sell your bitcoin when the price of bitcoin was high and your local fiat was also high, given you a more advantage of higher return but you didn't sell it that period. but you sold it during emergency when btc has dip and you currency to dollar has reduced, you will sell at lost which may be problematic. though it may be vise versa as the case may be but there is a need to have have emergency fund in Fiat than I bitcoin, for the sake of unforseen circumstances and immediate spending.