You're right, Emergencies doesn't give us advanced notice before happening,it's always takes us by surprise and for that reason alone,our emergency funds shouldn't be tampered with for any reason except for real time emergencies. Anybody who often diversify his emergency funds for other investments purposes is simply a gambler and might be doing so for quick profits .
People can change their initial plans but I think it's more possible when a person does not have any idea of an emergency fund or ignore to build up his emergency fund. In contrast, if a person already thought deeply about it, and actually built up his emergency fund, it's harder to withdraw money from his emergency fund and use it for other things like investment, trading or gambling.
I don't say it never happens, but it barely happens and people most won't break their own good initial plan by arbitrarily use their emergency funds for something in short term only.
Such a person is basically gambling with his investment. He is keeping the emergency fund in a position where the emergency fund can be easily lost or he faces an emergency very quickly. Then he will only lose his investment like a gamble.
We have said again and again, do not take any risk with the emergency fund, because the emergency fund can be directly involved in the investment. If there is a lot of cash flow, then you may be successful in protecting your investment in the initial stage of the emergency. But if the emergency lasts for a long time, your investment will definitely be at risk. So try to keep the emergency fund close to you in fiat money, so that it is easy to use the emergency fund in an emergency. Avoid the temptation of small profits earned from the emergency fund, because the reality is not as simple as you plan.