You seem to think that discretionary income and emergency funds are widely different, you emergency funds comes from your discretionary income the same way your investment comes from it as well, discretionary income isn't necessarily meant only for investment, the amount of discretionary income you decide to use to invest depends on how aggressively you want to buy bitcoin and after investing you can always put what's left from your discretionary income into your emergency funds, this is because an emergency fund isn't a part of your daily, weekly or monthly necessity, so you can only save for emergencies after you have taken care of what's necessary and once you have taken care of what's necessary you are left with your discretionary income which you then split between investing in bitcoin and saving up for emergency. Also, you don't save up for emergency indefinitely, after saving up for a few months worth of emergency funds you can decide to put the rest of your discretionary income into building up your portfolio and you can rise from investing on a medium level to becoming an aggressive investor, you should know that buying aggressively doesn't necessarily depend on how big your investment is compared to what others are investing but how big your investment is compared to your total discretionary income so the more of your discretionary income you invest in bitcoin the more aggressively you are buying bitcoin.
Your comment about not saving for an indefinite period for emergency funds basically implies that emergency funds should be limited in amount, which is correct. However, there should be a clear goal for emergency funds. So that it is understood that saving for how many months of expenses will be enough for you. If the emergency fund runs out in an emergency, you can get stressed. There are many who are suffer from complacency by keeping a small amount of emergency funds, which is dangerous. On the other hand, there are many new investors who do not consider the need for an emergency fund. This is understood only when the fund runs out and you are really at risk. You need to have a cash flow plan for at least 3 to 6 months or 12 to 18 months. Or you can set a threshold for an emergency fund by determining your safety margin. However, I believe that being financially secure is essential if we want to succeed in our investments.
Part of the reason that we may tend to not want to keep various back up funds in cash for more than 3 to 6 months of our expenses is because cash tends to lose its value, and the more of it you are holding the more your value is being eroded away.. yet when you are brand new to investing, and you don't have much net worth or many assets or much cash, you likely have to build at least a minimum buffer from your investments in cash.
The longer that you are investing, the more likely you are building up more and more wealth and you are not necessarily wanting to keep very much of it in cash, yet if you don't have any other income, then you might keep more in cash, versus if you have income, then you don't need to keep as much in cash, and even various investments that you have may well serve as back ups to your cash, so you might have an order in which you might cash out of various investments some are more liquid than others and some are more volatile than others, and if you have been investing for 10-15 years or longer, you might have assets besides just bitcoin and cash, perhaps. It is not necessary to do so, yet I believe that once your bitcoin is getting close to 1 year of your expenses or even more than 1 year of your expenses, you have the option to consider the extent to which you might want to have value in other assets such as stocks, bonds, property, commodities, cash/cash equivalents.
Some people come to bitcoin and they already have other investments and they will be left with a choice whether to continue to contribute to their other investment while adding bitcoin or to focus on bitcoin alone or maybe even to cash out of some of their other investments and put some or all of that value into bitcoin. Those are not bad problems to have, yet part of the choice will have to do with assessing the other investments in terms of their liquidiy, their volatility and their likelihood to increase or decrease in value with the passage of time. Presumptively we are mostly focusing on bitcoin based on our thougts/speculation that it is going to hold its value and/or potentially appreciate in value more than other assets and/or currencies.
I do think that it is fruitful to project out your cashflow (income versus expenses for 6 to 18 months into the future, and perhaps even longer if their are some reasons to do so, even though the 1-3 months are the most urgent and surely when we are within any biven month, we should not necessarily be thinking about whether we have enough money to cover every thing, yet we might see in advance that we have several bills coming due several months in advance and in order to meet the bills and to not cause our own emergencies (shortages of cash to cover the bills), then we likely would be able to see those possible shortages in advance by projecting out into the future by several months, sometimes 6 to 18 months into the future can help to identify short falls and/or possible surpluses that might play out during certain periods in the future and allow us to spend and/or save in accordance to making adjustments. When I was first starting to project my cashflows into the future (more than 30 years ago). I would make sure that my main account never went below $300, even during the lowest portion of the times, so that $300 was allowed to cover various mistakes or extra expenses and frequently I would see several months in advance that there was no way to keep the $300 buffer amount 3-4 months down the road unless I made various adjustments in my income and/or spending in the coming weeks... so that there might even be several expenses that are included such as a vague category like "$150 entertainment" "$300 anticipated extra lodging" etc etc etc.. I could sometimes make adjustments to the vague categories in order to make sure that 3-4 months down the road my cash buffer would not go below $300.
After a few years of using $300 as my buffer, there were times that I was stressing out, so I increased the buffer to $500, then maybe 10 years later, I increased it to $1k, and then there was a period that I had various business complications and/or arrangements, so increased it to between $2,500 to $3k, and then when those complications went away I reduced it to $1,500... then that $1,500 gravitated up to $2k, and so even now, I won't say exactly what it is, but the period of time that it was $1,500 to $2k was around 10 years ago. Using an Excel spreadsheet does help to make those kinds of projections, and to even see that many months the income and the expenses might be similar but then there might be certain expenses added or subtracted from time to time, too.