~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.
Your explanation and conversation are muddled because the biggest truth hidden behind your indications is that emergency funds are used only for investments 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.
No, emergency funds is not basically for investment infact that's not their primary purpose, just like the name implies it's used for unplanned financial issues in the future or near future for instance medical bills, auto mobile fixing bills or support for a bill that can't be taken care of by the discretionary funds, those are the duty of the emergency funds whereas funds that's mainly for Bitcoin investment is the discretionary fund.
The emergency fund can only serve as a discretionary funds in a case where an investor lose their job then get support from the emergency funds to be used as discretionary for the time being till the person get another job. @Out of mind, yes you're right the emergency funds would only be used for investment as protective measure when the investor can't generate discretionary funds for the time being.