Well, basically this is very important that having an emergency fund is very important for a Invest. When you invest in Bitcoin at a fixed price and then if the market falls, you can use that emergency fund for any necessary purpose. It is important to collect an emergency fund before buying Bitcoin, it will always be a good plan for yourself and it can benefit the investor in any bad time. I think such a plan would be a good step for real investors where they invest according to a percentage, save some percentage and leave some for an emergency fund. Many times this emergency fund is very useful to deal with emergencies, every person should have such an emergency fund plan that will always benefit them.
Your explanation and conversation are muddled because your indications suggest that emergency funds may be needed only for investment, which is largely untrue. This is where the disagreement lies because this fund has nothing to do with the rise and fall of Bitcoin's price, this means that even if you do not invest or if the price of Bitcoin increases after you invest, the need for this emergency fund to keep your investment intact is undeniable.
In fact this is a balanced part of the investment plan because its importance is given to avoiding excessive financial worries while investing and to investing continuously without any worries. As far as I know, never delay investing for emergency funds because you can buy Bitcoin in any season with discretionary income and will gradually be able to build up emergency funds for protective measures.