Emergency funds for some of them are not to be taken to invest, but rather emergency funds for their living needs when they are pressed by a disaster that occurs, be it a flood, earthquake or the death of a relative. So they can use the emergency funds for that, instead of selling assets/bitcoins they own. In fact, what you explained is not wrong, but the term might be better used as cushion funds or reserve assets that they can take so they don't miss the stage of their purchase.
Emergency fund is not recommended for investing in bitcoin but no bad to use it because put emergency fund in bitcoin have potential in the future price keep increasing than hold in pocket only, not really difficult for withdrawing emergency fund when saving in Bitcoin due put or hold in exchange wallet and when emergency happening to us we can sell and withdraw to bank account without take 10 minutes. No one can't predicting when happening with something urgent for us and my opinion better put emergency fund in bitcoin investment and seems the same when have parent hold or save their money allocated for children education. Hold in the bank can make it double although we start investing when our children under two or three years and take at seven or ten years later. Its very important allocated our fund for children cost but effective when saving or put in Bitcoin.
If you put your emergency funds into Bitcoin, there are chances that you will be forced to sell some of your Bitcoin when you did not plan. This has the tendency of harming your portfolio as well as your psychology especially when you realized you sold at a very wrong time. In other words, it is not a good situation to be as it is possible you might get too comfortable selling when you should be buying.
Since we cannot really tell how things will pan out in life, it is always good to plan against any eventuality. So emergency funds should be kept for what the title says likewise investment funds... this is the way to live comfortably today and at the same time plan for the future. There have been instances of people who use their school fees to buy Bitcoin with the hope that they will sell, make profits from there they can pay their school fees. Unfortunately, they bought at the peak and market never gave them the opportunity to see any reasonable profit. Some end up selling in regrets. There are many other bad habits people have that can be called gambling.
I was impressed by your statement above "keep buying BTC and revalue your position in 3-5 years from now" and yes. I think the DCA investment model should continue. Well, I want to know. Can Bitcoin get back $34,000 by the end of September 2023?
It's hard as we are now in September which is almost the end. I also doubt the price can get back to $30k by this month.
All can happen if one big news boosts the price such as Elon going back to accepting Bitcoin or another country accepting Bitcoin as a legal tender. But that is not easy.
Yes, DCA investment should continue as the price is still below $30k. It's a good price to buy

I quite agree with you on this. News affect price so much and so far, there is no strong news that will cause any rapid increase in price from now till the end of this month. The importance of capitalizing on the low price cannot be over-emphasized because price will drastically rise as we approach next year given the line of bullish events next year. A decisive DCA from now to December, can enable one accumulate sizeable Bitcoin.... this is my suggestion.