To the limited extent that Bitcoin helps Chinese citizens out-maneuver the capital controls that the Chinese government has tried to enforce, then it could be analyzed as a shadow of the Chinese currency, but since the action is illegal, the data is dark. Thus Bitcoin, and other crypto currencies, are the world's most opaque investment.
Is that bitcoin's problem or a traditional economists problem?
Behavioral economics does have frameworks for thinking about bitcoin price, but then again, behavioral finance is not traditional and highly controversial. For once, it dispenses with the myth of the rational investor (homo economicus)
So, how does behavioral economics supply a price for Bitcoin?
There are many stocks that belong to companies that have no mechanisms in place nor could they be reasonably expected to introduce mechanisms to directly return profits to shareholders. These stocks have the same form of "intrinsic value" as gold or Bitcoin: whatever the hell the next person is willing to pay for it.
Pretending that an underlying asset that doesn't throw off any yield or return of capital is somehow more rationally valuable than another doesn't make sense.
Whether stocks pay dividends or not is not terribly relevant, see Modigliani-Miller.
Thus, share prices are rationally anchored to economic reality. Of course, there's a lot of estimation involved, and people can get it wrong for a while, individually or collectively.
From that perspective, taking control of Bitcoin may have a measurable monetary value but as I understand the system the value isn't in the coins, it's in the miners.
Lets say I have a company with 1 billion dollar worth of assets and a 100 million dollar profit per year. I have issued 100 million shares during IP. How much is a single share worth? At the very least $10.
Next year I have a 1.1 billion dollar company. How much is a single share worth? At the very least $11.
You have 1000 shares worth $11000.
I can now either pay the profit out as dividend or not. Your shares will be worth less by exactly the amount that was paid out. Your 1000 shares will be worth $10000 and you will have $1000 in cash or alternatively I don't pay out a dividend and you still have 1000 shares worth $11000.
Where did that growth come from? With a company it's easy to answer. They sold more of their existing products. Released a new product. Reduced costs through technology. We have more stuff now. Investing in a stock helps a company indirectly even if stock buybacks never happen. The company receives better lending conditions from banks.
What about cryptocurrency? A currency shouldn't move in price at all. Where did that growth come from? From other people. Nothing new was created. Existing wealth merely gets redistributed.
As in "why is the price what it is". Saying "because of supply and demand" is useless, unhelpful pedantry.
In case you don't know, things like https://en.wikipedia.org/wiki/Market_manipulation exists..