Subjective value doesn't mean I can make up whatever I want, it means I value things according to the highest use to which I (the subject) can put them.
For Bitcoin that is only trade, and it has that value only because others value it for trade, and they value it for trade only because still others value it for trade. Do you see the circularity?
Who determines "the highest use to which [you] can put them" if not you yourself?
Your question about circularity...I think you've just described all money (including gold). Unless you mean that gold *also* has industrial uses: in which case...that's *descriptive* of how money has come about historically, but I'm not convinced it's also *prescriptive* for how it "must" come about...bitcoin being a case in point. Even so, math has industrial as well as other purposes. Why must it be a "physical" object? If it's purely to limit inflation, then that can also be accomplished with math...
You determine the value, but it's not a whim. It's not something you can make up however you want. If I decide that salt is worth more to me than gold & sell everything I own to buy salt, I will probably discover that in fact there are limits to what I can do with salt and the real well-being or satisfaction I get from the salt is less than I might have hoped. When I discovered this, I will have to sell or otherwise dispose of the salt, which reveals my low valuation upon experience.
