In an economy that is driven by Bitcoin, Bitcoin will be worth much less than it is today.
This argument relies on accepting a few premises. Also, it will become clear that "Bitcoin" doesn't just refer to Bitcoin.
1: Bitcoin's intrinsic worth is as a medium of exchange, not merely as a store of value.
Bitcoin is often referred to as "digital gold". Consider the role of gold in the economy though. It's price goes up and down, and over time doesn't keep up with economic growth. Instead, it's used as a hedge against economic catastrophe, the idea being that if the economy completely tanks, gold's physicality, rarity, tradition as a valuable commodity, and lack of tarnishing will enable its possessor to retain some value where contracts and paper fail. Bitcoin lacks this physicality, and instead relies on the maintenance of a functional, open, and widely accessible Internet to use - one that will likely not hold up in many the scenarios gold is used to hedge against. That makes its use case as "digital gold" narrower than gold itself.
If Bitcoin is to be a workable store of value, it will be so only inasmuch as its utility as a medium of exchange lends it value.
As a medium of exchange, Bitcoin (or cryptocurrency generally) promises to out-compete fiat currency in a number of ways.
2: A cryptocurrency that succeeds as a medium of exchange will allow for immediate, cheap transactions, and interface directly with other digital assets.
In the success scenario, you will be able to buy almost anything with bitcoin, and transact instantaneously. You will be able to buy and sell tokenized digital assets, like DAO's, contracts in prediction markets, and much more. And you will be and to digitally move your wealth into and out of conventional assets with ease as well.
3: Because of the ease of transferring to and from other assets, there will never be a reason to keep raw Bitcoin sitting around in your wallet.
Think how dollars work. You have a jar of change. You have cash in your wallet. You have money sitting in your bank account, perhaps more than one. Business too. Why? Because banks and governments make it hard, time-consuming, and expensive to turn your dollars into interest-bearing assets.
But with crypto, you ideally will be able to automatically convert your money to and from a variety of economically valuable assets. There will never be a reason to keep raw crypto sitting around instead of immediately going to digital market to purchase a share of an asset.
Instead of being the place where you keep your wealth, Bitcoin will be the interface between your different stores of wealth and markets. (Hmm, this is starting to sound a little like Bitshares...)
Thus, a successful cryptocurrency medium of exchange will have a market cap that is a minute fraction of the market cap of fiat currency.
Since a successful future Bitwhatever will make transactions cheap and assets easy to buy and sell, nobody will hang onto it, so while the transaction rate will be high, the market cap will be small.
Since the M1 money supply of USD is only ~15 times Bitcoin's market cap (what's today's price, anyway?), Bitcoin is substantially overpriced.
The M1 money supply is a measure of US dollars in circulation that more or less gets at the number of actual dollars there are, not just physical dollars, but also not derived assets. It's not the best comparison for Bitcoin, because, well, there are other currencies, but there are also other cryptocurrencies.
If Bitcoin ever truly out-competes the dollar, it will do so only by facilitating super fast super cheap transactions and allowing people to avoid leaving their money in currency. In such a case, its market cap should be thousands of times smaller than fiat currency.
Either the scenario described above comes to pass for Bitcoin, or it comes to pass for some other cryptocurrency, or it doesn't come to pass at all. In any case, Bitcoin's price cannot be justified. If it doesn't become a superb medium of exchange, it is worthless. If it does become a superb medium of exchange, it is worth something, but the fundamental price is much lower than it is now.
Caveats: Why I might be wrong
A) Fiat currency might crash. In that case, Bitcoin's fiat prices could soar, though its inflation-adjusted price may not, certainly not in the long run. This crash only happens if governments are too stupid to prevent it. (Taxation allows governments to force demand for their currencies.) But governments can be pretty stupid so who knows.
B) A host of bots could emerge that make so many transactions that it drives up the market cap out of necessity. This is sort of equivalent to saying that there will be immense economic growth, so again, it might just be better to invest in the right assets.
Disclaimer: I am not an economist and the reasoning given herein has not been peer reviewed for academic consistency.