[testific8]

bitcoin and related systems are a solution to the double spending problem. Perhaps a flawed solution based on the information we know now, but it is a solution nonetheless. some related systems such as monero, zcash, and GNU taler make attempts at ensuring spender privacy, like cash.

but the computational power is nessisary for the network to function in a manner that is provable to new nodes. Because you can use a digital signature to confirm a transaction happened after some time, but not before some time.

I don't think cash is a solved problem within the context of computer networks. If I could transfer money using a program by using a digital signature, I would be satisfied, but anyone who can get access to my credit card numbers (and name, billing address and other open source info) can make purchases in my name. And you of course must rely on the fractional reserves of some central entity.