Some blockchains have private transactions and very good at it indeed.

https://bitinfocharts.com/comparison/transactionfees-btc-xmr...

Monero has fees of six cents it looks like and a novel and private way of performing transactions.

https://en.wikipedia.org/wiki/Monero

https://en.wikipedia.org/wiki/Ring_signature

Layer 2s such as Bitcoin's lightning network do not use a public ledger for their transactions. The only thing public is the transaction that opens a payment channel, everything after that happens as peer to peer messaging across the network.