Things get value from how they are used, not vice versa. Bitcoin is used as a way to transfer money. It is not money but a token used to move money; as such, it needn't retain its value for more than the time it takes to buy, transfer, and resell. A token used to move money has value because moving money is a service for which people get paid. Owning bitcoin enables a service provider to move money, so bitcoin has value.

The peer-to-peer part is the problem. To move money using Bitcoin, you buy some from an exchange and transfer it to your payee, and your payee then resells it to an exchange. Each transfer of bitcoin is peer-to-peer, but the transfer of money using bitcoin involves third/fourth parties, depending on whether the payer and payee use the same exchange. Bitcoin is thus a franchise to be that third or fourth party, and the value of bitcoin depends on value of that franchise.

Because the bitcoin network is so slow, workarounds like the Lightning Network try to reduce the actual number of transfers. Trouble is, the fewer actual transfers occur, the fewer bitcoin an exchange needs to own. For now, exchanges still need substantial inventories, so bitcoin for that inventory are expensive.

One reason bitcoin are expensive is that HODLers are reducing the float. The real question is whether the system will ever equilibrate at a level where the price stops rising and HODLers start selling. And it's not clear who will validate transactions for what compensation after 2040. Still, if bitcoin becomes a better way to move money than the banks can come up with - something I doubt, but we're just theorizing here - bitcoin will be valuable as a rentable asset, pretty much like airplanes and railroad cars.