I feel like this falls into the classic blunder of smart dumb guys throughout history of using aggregation and abstraction to obscure what's actually happening.

It's not technically the same as chasing losses because the bet doesn't technically resolve until you try to sell your Bitcoin. Unless you're selling your stake and only then deciding whether on not to buy more, the theoretical final value of your Bitcoin could be anything. In that sense, DCA does make some sense in the hypothetical final accounting. UYour payout is whatever price you sell at, and your buy-in is a weighted average of the prices you bought at. For something like a stock portfolio where you actually have reason to expect the overall value of your investment to grow over time (because the economy generally grows and your portfolio is spread across a broad swathe of it) the math does work.

But the problem is that it doesn't address the fundamental problem of crypto investing, which is that crypto is worthless and crypto bros are usually looking to concentrate their assets in this worthless category. "Look at my average cost go down!" isn't actually a relevant response to "why are you throwing more of your money into a fire?" In average terms you may have paid less per unit you own, but in absolute terms you're still throwing good money after bad.

Averages, samples, models, aggregates, whatever form it takes, the tools we use to track and evaluate the world don't magically tunnel through space and time to change it. In terms our very good friends would recognize: the map is not the territory. But especially in finance it seems like making the map look the way you want gets treated by smart dumb guys as though it's the same thing as changing the territory itself to be more favorable, when in truth they're either finding a prettier vantage point for your landscape photography or else straight up lying and sketching in a non-existent beach.