Actually stores of value need neither, though our disagreement may be at least partly down to semantics.
A store of value does not have to be inherently secure. Rather the political, legal and economic structure must be such that it would not be trivial to take away your property by force. Actually BTC is the only store of value that has built in security features - but as you pointed out these are not sufficient.
A store of value does not have to be backed by anything to retain purchasing power. The only thing that needs to 'back' it is the expectation that the public perception of its value will persist.
NEITHER? Are you serious? You think an asset can be an effective store-of-value if it lacks both Security AND Stable value? Are you arguing that store-of-value is based on NOTHING BUT AN INABILITY TO GROW THE SUPPLY, cause that's what it sounds like.
Lets compare, Crypto-currency is a Fiat currency protocol that provides excellent counterfeit protection and modest protection against identity theft (private key signed transaction, but constantly hacked), and has no backing. The strength of these features is depended on the size of a distributed computer network and BTC has the strongest network.
National Currency is another Fiat currency protocol that provides strong counterfeit protection, strong identity theft protection, modest fraud protection and modest theft protection. And it is backed by legal-tender status and by the collection of taxes. The strength of these features is based on the size and power a Nation-State and the United States is the strongest State.
So your arguing that throwing away all protection of fraud and theft, AND all backing to get slightly better counterfeit protection will actually give a stronger store-of-value. This is absurd the huge gaps in BTC's security and lack of backing make it a terrible store-of-value compared to the money of a nation-state. People need to stop confusing speculative GAIN with store-of-value, easy-come easy-go, a store-of-value dose not FALL OR RISE rapidly, store-of-value = stable value.
And your final comment about 'backing' something by the public expectation of value is simply laughable, no one with a clue as to the meaning of the word 'backing' would call fickle public expectation a backing, that is the exact OPPOSITE of a backing. Without a backing public expectation is like a ball at the top of a hill, as soon as it begins to roll it accelerates as BTC has consistently done. Something with a backing is like a ball in a valley, when it moves it's pushed back towards equilibrium.