The size of your emergency funds will determine the level of problem or emergencies that it can solve. You can't have $500 in your emergency funds account and expect it to solve a problem of $1000. It is wise for an investor to continually add to their emergency funds account as they keep getting resources. It is simple logic, it doesn't have anything to do with believe or whatsoever.
Your emergency fund is proportional with total money you have.
I don't think your emergency fund is proportional to the total money you have. Surely a person must have a source of income which is always higher, from hence emergency fund, Bitcoin amount for investment and discretion fund is drafted out or gotten from. So surely there could be times when the emergency fund would have increased to a certain level, to the extent of competeting with your source of income but that doesn't mean it is always proportional. There could even be times when you ungrade in financial strength maybe your source of income increasing from $1000 per month to $5k per month and hense you may decide to increase your emergency fund becomes there is an increment. So there is surely no comparison for both.
Assume you have only $1,000 totally, you can not assign an emergency fund with $1,000 or 10,000 but it is possible to have an emergency fund at $100,000 if your total wealth is several billions of dollar.
I don't understand the point you are trying to make, how can you have a total of $1k as discretion fund and use all for emergency, of course that will be stupid of such person. It is advisable to used lesser amount from the discretion fund to set aside emergency fund. Let say if the $10k is the discretion fund, there is a possibility of setting aside emergency fund of $500 every week or possibly $2k or $2.5 per month since the discretion fund is capable to settle other neccecity.
If you have plan to add up more money to your emergency fund, it's good and you also have to be clear that how much is acceptable for your emergency fund and when you reach that point, you can feel safe enough and reduce severe need of adding more money to that fund.
No amount is enough to fell safe of reducing the level of stacking emergency fund. You should know that the amount of emergency fund you have will determine the gravity of of problem you have. Surely we don set problem for our self but we can only be prepared for it by keeping a reasonable amount when the problem arises. A person can decide to reduce the rate of keeping emergency fund when he has reached the pick of $100k and may incure a Loss of $200k in his business. By then will the person knows that he had never even had emergency fund all this while. Just treat emergency fund as a normal routine just as you eat every day, be also ready to fall sick one day just as you should be reasy to incure loses. Like business loss, health failure, natural disasters and many More. All this don't surely tell you how much to keep as emergency. That's why you must not nurse the idea of over accumulating limit in emergency fund.
It's good if you can add more money to it but after that safe point, it's not terrible if you won't add more money for it.
Like I said you don't really need to have a safe point of not setting aside emergency fund.