Is encryption really necessary for blockchain to work?

Bitcoin does not use encryption, and is not necessary to ensure ownership of the coins. The ownership of the coins is demonstrated by digitally signing a transaction with the owner's private keys. The signature can be validated by anyone using the owner's public key.

The encryption confuses the data of any person who is not authorized to see them (decipher them). Bitcoin can not encrypt the data stored in the blocks because the data must be validated by everyone Users (to avoid double spending).

Encryption is used, however, in wallets to secure one's private keys, but that depends on the software of the wallet and how they have chosen to implement this type of protection. For example, the Bitcoin Core wallet has a way to encrypt the wallet with a passphrase, see RPC Documents – Encrypt wallet, but this is not essential for Bitcoin, users can use any wallet application.

Edit: As noted in the comments, a point of confusion is that Bitcoin uses cryptography by elliptic curve, not RSA. This means that a digital signature in Bitcoin does not use encryption as RSA does, but an algorithm called ECDSA.