Labor theory of value is insanely flawed and has absolutely nothing to do with Bitcoin's Proof of Work.

All value is subjective because it only exists in our minds, all people value the same things differently, and the price is just a consensus between the seller and the buyer. Labor theory of value treats value as some sort of objective physical property, and it fails to describe the reality because it totally ignores how economy actually works.

It completely fails in the case of Bitcoin, because the total network hashrate is driven by the price, not vice versa. Miners add more ASICS because they see big profitability, they never add ASICS hoping that this will drive the price higher. This is because the market doesn't see PoW value as linear, if the network is already secure, the security gains will start to diminish (even though the cost of attack scales linearly).

Labor alone is not the source of value, other people need to view it as useful in order to create value, and this is not a binary value, it's a scale. Bitcoin price increased so much since it's launch because more people became aware of it, more people started to want it, while the supply was decreasing.

I'm pretty sure that Satoshi was familiar with Austrian economics and maybe was even inspired by them, because PoW is based on supply and demand, not labor theory. If Bitcoin was based on Marxist ideas, it would have constant difficulty and constant reward and fixed fees (or no fees).