Medical records and voting slips aren't valuable and can just be stored in a distributed database. They either have no need for cryptographic verification or are impossible to implement in a decentralized and secure manner (elections, for obvious reasons)
Actually there
are use cases where everything (even value changes) has to be recoded and every record must not be changed ever.
Not as many as some devs would like, but still, they are. For example EU seems to use EBSI (you may want to translate and read that topic for context, shortly, Romanian vote counting was delivered from voting centers via ETH blockchain)
Hyperledger Besu is an enterprise-friendly Ethereum client suitable for both public and private permissioned blockchain network use cases. It is also EVM (Ethereum Virtual Machine) compatible, which signifies that EBSI can support the deployment of smart contracts written in Solidity, executable by the EVM in a decentralised manner.
Without currency, there is no blockchain.
Private blockchains can be interesting even if they don't hold money. Private smart contracts on public blockchains can be even more interesting.
Public blockchains, yes, you're right, need to pay for the PoW hence they need to hold money/block rewards.