What do you mean by one BTC will remain one BTC even if the demand decreases? Are you not aware of the supply and demand rule and how it works? The price of Bitcoin or any commodity or thing increases if that commodity or thing gets a higher demand if it has a limited supply, and the same thing happens in the opposite way if the demand drops.
The interest rising or falling may don't have any effect on the network and it will obviously continue to work stably, but that does affect the market in general, in terms of monetary value. Bitcoin and any other cryptocurrency with a limited supply need higher demand to have a further increase in its price.
Suppose the demand for dollars decreases, how many dollars will one dollar cost then? Five dollars? Ten? One hundred? As long as you count everything in dollars, there is a price for this in dollars, but the dollar itself cannot change relative to itself. By changing the paradigm, and starting to look at the world through bitcoins, and not through dollars, in the same way we have a situation where 1 bitcoin remains one bitcoin forever. It doesn't matter whether demand is rising or falling at any given moment. Unlike the dollar, the number of bitcoins will not increase or decrease from this.