Great question. We can decompose bitcoin's price fluctuations in USD terms into two factors:

I think we can agree that the purchasing power of bitcoin in real terms is not presently constant and that it is higher today that it was five or ten years. 1 bitcoin is legitimately worth more to the market than in 2013.

Why is this? The market requires a certain real rate of return for every asset in the world. Bitcoin is no different. The rate of return the market requires is a function of bitcoin's perceived riskiness and the compensation required for that level of risk, given the opportunity set. If the attractiveness of the opportunity set changes, or bitcoin is viewed as more or less risky, the required real rate of return will change.

This will literally change the purchasing power of bitcoin in real terms, with or without a fiat system. When the required real rate of return falls, the price of bitcoin in real terms rises, until the required and the expected real rates of return are the same.

Now, to your point, what happens in the "upcoming non-fiat future"? Well, the required real rate of return will still not be constant. At some points in time, the opportunity set in the market will be more attractive, and at other times, it will be less. If an incredible new technology is discovered, for instance, that creates tons of attractive new investment opportunities, the required real rate of return will rise. Conversely, if there is an adverse economic shock, like a global pandemic, that wipes out opportunities, the required real rate of return will fall.

For this reason, as long as the world remains uncertain, and there are opportunities to be discovered, bitcoin's value in real terms will never be constant.

This is perfectly acceptable when thinking about bitcoin as a store of value, but it is problematic when considering BTC as a unit of account. If Bob agrees to sell his labor to Alice for a given monthly wage, Bob wants to know how much purchasing power he will be receiving, and Alice wants to know how much purchasing power she will be spending. It is in everyone's interest to use a unit of account whose future value in real terms is as certain as possible, which is why BTC is a poor unit of account.