The notion of property rights is only relevant with a central authority who is able to enforce it. Which could be a nation state, tribal chief or a lord. In the jungle you only own whatever you are able to defend. Even your own life.
The same was true for salt, and many more local kinds of money that existed.
It's also the same trust you need for fiat money. This, and trust that your government won't create a huge lot of it in an instant (slow rates of money creation are fine). Turns out that governments have a lot of leverage to enforce the first, more relevant kind of trust, so the total trust required decreases.
The idea of cryptocoins was to remove the trust on nobody creating a lot of money very fast. But in doing so, they also lost the leverage to enforce that people will accept it.
The innovation of bitcoin is precisely making this statement no longer true. The "property" might only be digital data, rather than physical things, so you can argue that it is no longer true in only a limited context, but it is not longer absolutely true.
Maintaining BTC itself requires physical inputs and physical property rights. You need fiat to buy energy. Your house with mining rigs needs enforcement of property rights.
> You need fiat to buy energy.
This is a circular argument and not true. You can buy energy today with gold or bitcoin.
For 'fiat currency', it's the fact that the state has a monopoly on violence and has decreed both [A] that they will accept the fiat currency for fulfillment of tax obligations, and [B] that they will not enforce a claim of debt if you have offered to pay it in fiat currency and the debtee didn't accept your offer.
For gold it's the fact that gold is considered intrinsically pretty by some, and has industrial uses.
The same can be said for iron, wood, or even air - but those are far less rare. Wood has value just as gold does - it's just that folks tend not to trade trailers full of wood as a fungible because it is unwieldy.
Stocks have intrinsic value too: It's a tiny voting share, and gives the right to enjoy a share of dividends.
Bitcoin has __nothing__. Whatsoever. It's real easy to look at the ridiculous price of stocks in companies that make it incredibly difficult to use your vote and which never pay out any dividends, or the sheer unfathomable levels of business done in terms of USD or EUR and how it seems to dwarf the intrinsic, and conclude that the intrinsic is just not important...
But is that a jump you can make?
As you said:
> I accept 100 euro bills for my labour because I believe I'll continue to be able to trade them for food and shelter.
You sure? Maybe it's 1% 'because I have absolute guarantees I can pay my taxes with this, and I have a guarantee that I can trade them for food and shelter because if I pay my bills with dollars and the recipient no longer wants them, they have no legal recourse to force me to make good in any other way'. Presumably you have certain outstanding debts that work like this (if not just simply your tax bill, which is inevitable, then your power bill, your rent or mortgage, etc), so that euro bill __already has value__ the moment you receive it. You can take your mental bookkeeping of 'oh yeah the month is halfway through so I absolutely do, unambiguously, owe my bank half a month's mortgage at the very least', and immediately reduce that amount by €100,-, given that you are holding a €100,- bill in your hands and the state has decreed that they will tell the bank to get fucked if they decide they no longer want to accept your euro for paying off that mortgage.
As for Bitcoin, the original Bitcoin paper talks about replacing trust with code, and I just don't buy it. Sure, you can trust that Bitcoin aren't spent more than once and all that, the maths take care of that. But it fails to consider all the institutions that integrate the Bitcoin world with the rest of social/economical reality, and all that arises there like price volatility, transactions taking forever, exchanges getting hacked, and that Bitcoin-as-a-casino, excuse me, object of speculation, has a far bigger impact on its day-to-day than for e.g. the Euro. The paper doesn't consider that reality at all, but those things mean that 1000EUR worth of Bitcoin is a lot less useful than a stack of fifties.