I agree with you that buying a fixed amount of bitcoin will ruin his bitcoin accumulation plan because if he sticks with buying a fixed amount of bitcoin weekly or monthly, he will end up not making a provision for emergency funds. For instance, If he bought his first bitcoin of 0.003 BTC at $42700 and wants to buy another bitcoin with a fixed amount of 0.003 BTC and the bitcoin price is at $50k, he will have to pay more money to accumulate the 0.003 BTC, which will make him use most of his weekly or monthly salary to accumulate the fixed amount of bitcoin, and he will depend on his bitcoin investment to settle his financial needs because the strategy he adopted to accumulate bitcoin did not allow him to keep an emergence fund. I see this as gambling because he might miss out on owning a bitcoin.
I don't know if the DCA method can be calculated in terms of the Bitcoin quantity because what I do know is that it is based on dollar amount that is why it is called dollar-cost averaging.
If an investor decides to buy a fixed quantity of Bitcoin per time irrespective of price fluctuations, that is possible and achievable as it may be that he would have set a target to achieve in terms of Bitcoin quantity. For instance, someone can set a target of owning 1BTC before his 20th birthday and may decide to be accumulating 0.01BTC weekly or monthly as the case may be. As expected, he would have made adequate financial preparations for this, bearing in mind that while following his plans he will also pay his bills and also set up some reserve funds. I do not see anything wrong with setting such personal targets neither does it mean that he would not have factored in price fluctuations in his planning.
I look forward to seeing what others will have to say about such plans, if it qualifies as DCA or something similar to it. I'm with my pen and my note, time to learn something new.
For me I really don't think an investor can be able to buy a fixed quantity of Bitcoin within a stipulated time interval reason being that the price of Bitcoin might keep soaring higher thereby he can't afford buying same quantity of Bitcoin as the previous one he bought while the price was lesser and moreover, just like your illustration about if a investor wants to achieve 1BTC on his 20th birthday and let's assume that the birthday would be in three years time and his DCA every week is like $1000 and from his speculation of the price of Bitcoin in that three years is like $150,000 and let's say in that 3 years the price of Bitcoin now reached $200,000 so definitely his DCA in that three years will amount $156,000 so you can see that he didn't meet up his targets of owning that 1 BTC on his birthday after his speculation 3 years back.
However, any good Bitcoin investor should just keep accumulating bitcoin rather than making speculations and also make sure that they have a steady income that will aid their DCA and also make sure they have alternatives to their source of income so that they won't miss out the DCA, only then can they record huge amount of Bitcoins in their portfolios and make reasonable profits out from it.