It's not a labor theory of value at all. There is no specific amount of work that has to be done. You could run mining software on your phone for 5 minutes and find a block which rewards you with bitcoin. It just generally requires more effort than that to acquire scarce things. If gold was just freely available it would not be money.
Discussion
Yes, scarcity is a requirement for something to have economic value.
That does not mean that work has to be done or that the scarce thing derives its value from the work done to obtain it. Those are fallacies.
I agree that making up records of new Bitcoin units is expensive. So is digging a hole and filling it back up. If I could prove that I had dug a hole of a certain size and filled it back up, would that receipt be a candidate to use as a money unit?
If the only way to reverse the transaction history is to do more work than was done to record the history in the first place then the setrlement assurances provided are a function of the cost of the work done.
settlement of what?
it's easy to build a better mousetrap when the mice are all in your head
Money is valuable because it can facilitate trade. It has nothing to do with how tagible it is. Gold's tangibility has nothing to do with it's value as money. All other metals would be money too if tangibility had anything to do with it. Tangibility actually makes it worse at being money in a digital economy.
But the reality is that none of this bullshit matters. Bitcoin is going to keep working & keep being money whether you understand or agree or not.