The answer to this question is a big and resounding No. I have read several arguments using proof of work (PoW) to justify Bitcoin value, and this is wrong as the Theory of Subjetive Value demonstrates: No matter the costs of any good, the market will assess its value depending on its utility. A useless thing won’t have any value, no matter how costly it was to produce the thing.
Terms such as “accumulated energy”, “energy density”, “accumulated work” have no causal relationship with Bitcoin’s value.
Proof of work is a mechanism to ensure that all added transactions to the Bitcoin ledger are valid. Any attempt to add unvalid transactions (i.e. mainly double spends) would be rejected by the network. PoW ensures Bitcoin scarcity in the sense it avoids double spends.
The beauty of PoW is not only that is very easy to verify, but also that it is a naturally irreversible commitment. Each time a valid block is added, the Bitcoin protocol opens an auction to perform the task of adding valid transactions in the next block in exchange of a specific Bitcoin reward. The rules of the auction is that all participants have to incurr on irrecoverable costs in order to be able to bid, so fake bids are not possible. PoW is an irrecoverable pledge, and as such, it shows the strongest commitment possible towards adding valid transactions.
In order for Bitcoin to remain decentralized (i.e. immutable), it cannot rely on trust to secure the immutability of the ledger, so the best way to outsource security is to open a fully public auction to perform the task of adding valid transactions where in order to bid the strongest commitment is required, and as of today’s technology, the most efficient mechanism to achieve that commitment is Proof of work.
Proof of Stake, which would be a traditional pledge, is not irrecoverable by nature. Irrecoverability has to be artificially built in order to match the level of commitment that PoW inherently offers.
So far, PoW has proven to be the most efficient and reliable mechanism to deliver a high degree of immutability and no other technology seems to come close.
Anyhow, at the end of the day, what the Bitcoin user expects is transaction reliability and the certainty that scarcity remains as specified by the system, no matter how it is achieved or how much did it cost.