I agree with you that the important thing in bitcoin investment is the amount of income you earn and also the amount of bitcoin you are able to accumulate from it, but the aspect of waiting to buy every month end may not be the best option or that is not a wise investment approach. For me if a person recieve salary it is not good to invest once every month but we can mitigate the opportunity by splitting it across the week. For example if a person recieve salary at the first month of resumption, he can fix on how to split his fund into the following part, 1 for bitcoin investment 2. For emergency 3. reserved fund to use for the purpose of family expenses and also for buying bitcoin every week(DCA), buy the dip and of course lump sum till the next month of his salary which is the 4th week to enable him accumulate bitcoin at ease, than investing agresively and sell later due to lack of proper planning. Sothat he can take advantage of buying the dip in some week from his reserved fund than just investing once in Bitcoin and using the remaining amount on feeding and or meceleneous expenses.
I see no reason dividing your your money to invest weekly since it will still amount to same figure, for example if you want to invest $100 monthly when you receive your salary you can just use it at once than dividing it and still use it to accumulate weekly, the only time you should invest weekly is if you are receiving your salary on a weekly basis and from your analysis you did talk like someone who remembers that when ever we receives our salary the first thing we should do is to remove money for the running of the house like paying of taxes, electricity, water, stocking the house with food, paying rent etc, then Discretionary income being the one lift should be used to invest in Bitcoin.
When you receive your salary monthly and you decide to remove the one for Bitcoin and then divide it so you can then be using it to invest weekly there's a high tendency that you may even use it for another thing with the hope of returning it which may never happen there by reducing your accumulation percentage for the month.
There are several reason someone might want to spread the investment over several weeks or months as the case may be and it is usually a case of personal preference. One notable reason I can come up with is to get filled at different price point which may result in collecting more Bitcoin with the same dollar amount. For instance, in a market that is generally in down trend, dividing the funds and spreading the investment will make you get some coins at lower prices which will result in more Bitcoins. The reverse might be the case for a market that is generally in uptrend and this comes back to personal preference even though the overall goal is to be optimally invested in Bitcoin.
I don't see much difference between monthly and weekly DCA, and the choice for which to use depends on the cashflow. For those earning monthly income like salary, going for monthly DCA is best so that as soon as the funds are received, the part for investment are immediately converted to Bitcoin and transferred to a safe wallet. On the other hand those running business and seeing money daily can go with the weekly DCA as this may resonate more with them such that at the end of the week when they balance their books, they can easily set aside the funds for their Bitcoin investment. So the cashflow play important role but there could be other factors too that may inform the choice and investor will use.