Cryptocurrencies solve spam problem, not trust problem. No one can spam the network with new write data (transactions) because spam would become expensive. Although people still do, and Ethereum is full of spam tokens, meaning the transaction cost is still too low. This was also the use case of Hashcash, predecessor in proof-of-work, and was designed to solve email spam.
You are paying either
- Block space: your transaction to be included in a block
- State: modifying the world state (EVM in Ethereum)
Trust problem is solved by various other means, usually on libp2p level, by banning node (IP addresses) that send you bad data, which you can verify by comparing it to data from other peers.
Cryptocurrencies slow down the rate of data not because of spam but because a slower rate means a higher consistency across the network: cryptocurrencies' goal is to agree on a consistent state with peers who do not want to negotiate. If the consistent state is pure garbage then that is not a problem for blockchains, because from blockchains' point of view, everything is fine.
Spam is not a function of rate but of content. Spam can absolutely be sent in a blockchain, as you say, and making the price higher only makes both spam and non-spam more difficult. Spam for me might be actual legit information for you.
Hashcash is another beast, it only has the proof-of-work part, not the money part (contrary to its name) so it's not comparable.
They also solve the trust problem through consensus using proof of stake. If there is enough financial skin in the game to behave correctly, then that should be enough to make sure that results are not tainted.
You are paying either
- Block space: your transaction to be included in a block
- State: modifying the world state (EVM in Ethereum)
Trust problem is solved by various other means, usually on libp2p level, by banning node (IP addresses) that send you bad data, which you can verify by comparing it to data from other peers.