Hopefully we can attempt to maintain enough funds that we never have to tap into our emergency funds, and surely we know of people who seem to be having emergencies every month or every other month, and if we look more closely at why they are having their emergencies tends to be that they are not managing their cashflows well and/or they are not maintaining enough cash reserves, which like you suggest that the emergency funds should not be touched absent some kind of a real emergency, yet if someone puts themselves into a situation in which they do not have funds beyond their emergency fund, then they will end up tapping into their emergency fund way more frequently than they should be doing (especially if they were to have better cashflow management practices in which they have other funds to tap into based on variances that they might have in their income versus their expenses).
The more known variances in discretionary income then the more justified a person is to keep larger amounts of back up funds to account for such already known variances.
I agree with you JJG, some emergencies people keep having over and over again aren't to be grouped under emergencies any longer since you're aware it keeps recurring, you'd have to add it to your expenditure budget and try being better at your cashflow management to make provision for such expenses even before it presents itself. When such expenses are periodic, then you dedicate a variance of reserve funds to it and can build that variance to entertain it twice so you're not immediately under pressure to rebuild that reserve fund immediately after attending to it.
Understanding yourself and your expenditure patterns would help you employ a good cashflow management pattern to take care of your constant expenses, then create various kinds of backup funds for periodic expenses and be able to reserve emergency funds for pure emergencies only while still remaining committed to your Bitcoin accumulation journey. Everything boils down to proper planning.