~snip~
With same investment capital, you can invest gradually or aggressively, it's my thinking, that means I disagree with you.
Investment aggressively or not, it does not require to have extra (additional) source of income or investment capital. It's only matter that whether you want to DCA gradually or want to purchase bitcoins aggressively. Assuming with same investment capital as $1,000, you can gradually DCA in 10 months or your can purchase bitcoins more aggressively in 5 months or 3 months or 2 months.
Of course with DCA strategy, it's always better if you can have regular investment purchases and can have new investment capital with time rather than 100% rely on your investment capital at beginning and plan how to use it with time. Like you can start with $1,000 investment capital, plan to use it for purchasing bitcoins in 10 months, but it's better if with time, each month you can save part of your income and have like $50 or $100 more new investment capital. That will sum up your investment capital to bigger than $1,000 with months.
If a person has lump sum available, such as $1k to get started, and maybe he has an income in which he can buy $100 per week in bitcoin, then with the extra $1k, he does not need to invest through DCA, he could buy right away and/or he could buy at the dip (if the dip happens), so he has choices of the three different styles, and DCA is not always better if you already have a lump sum of cash come available to you. One of the reasons that so many people use DCA is because it is much easier to tailor some kind of a buying amount that goes along with their regular income coming in and their expenses, and so DCA also will allow an adjustment every week or whatever period that a person chooses to buy bitcoin under that kind of an approach/practice.
I think the aspect of discretionary funds discussed by you is very accurate. You do not need extra money to be aggressive in your investments but the extent depends on the level of risk that you can afford to undertake using the funds that you would not mind losing. You can either DCA or buy more aggressively using your existing discretionary capital depending upon your level of comfort and the market environment.
DCA is effective in the process of averaging against volatility and putting purchases in an ordinary income stream, however,
when you have a lump sum, it may be worthwhile to buy on the downside or buy more actively. It all depends on whether you have an effective plan and with a clear plan, you should not touch on monies that are likely to impact on your necessities. Basically, both strategies can be applied using the same capital, it is primarily a matter of timing, risk-taking, and disciplineness when using discretionary funds.
If you say buying on a Lump sum is worth while buying on the down side then to me you are describing buying the dip and not buying with the lump sum, because talking about buying with the lump sum has nothing to do with the market conditions but rather an investor decision to buy immediately with the available Lump sum amount irrespective of the market conditions,