I'm a little confused here. You say that bitcoin and fiat have no value for direct use, with which I agree. You then say that fiat does not work as a store of value. But then you imply that bitcoin can be a store of value that will suck in all of the extra stored value of the housing market. Why wouldn't bitcoin and fiat be the same in this regard? Yes, bitcoin has limited supply, but why does that mean that it should be considered a safe store of value (it would have to be considered even safer than real estate to suck in its stored value)? Or are you thinking of a future in which bitcoin basically becomes the reserve currency of the world, or at least the dominant currency of a particular country or region?
The difference between fiat and bitcoin is precisely that fiat is unlimited, and bitcoin is limited in supply. Since fiat is unlimited in supply, it can not be used as a store of value. Each time the supply is doubled, the stored value is halved (well, after the new fiat is dispersed). This is the main difference that bitcoin makes. It is in effect now, no need to wait until all others use bitcoins, if they ever will.
You are not telling the whole truth here. Your point that each time the money supply increases, the value of money decreases is only valid if all other things stay the same. If the money supply stays on par with the economy growth, there will be no decrease in the purchasing power of money. So fiat supply limitlessness is not enough per se to make it different from Bitcoin as a store of value.
The parameters I hold invariable in the consideration, is the number of people and their holding preferences (the saving rate is 0, or the amount saved does not change).
I do not consider economy growth as input to the money value function. Some do, but that is based on flaky statistics, which are trusted even when they fail. I consider the growth thing as an allegedly plausible way to get out of the current mess.
The value of the money is the supply (people willing to part with their money), and the demand to hold (people offering things for money because they want to hold more money, e.g save money).