The answer is simple: to build next-generation wallets that combine the advantages of a smart contract and an EOA account.
Today, most wallets (e.g., Metamask) are typical EOAs based on a private key. This model requires signing every transaction with the private key, making it cumbersome for users to interact with the wallet. Moreover, losing the private key means losing access to the wallet.
On the other hand, there are alternative contract-based wallets (Gnosis wallet). A smart contract allows implementing custom wallet logic, such as multi-signature functionality. However, users of such wallets still need an EOA account to call smart contract functions and pay gas fees.
Important! An EOA account is required because only it can initiate transactions in the blockchain. An EOA account signs transactions with its private key and pays gas for their execution.
ERC-4337 combines the features of EOA-based wallets and contract wallets by using pseudo-transactions instead of regular transactions. This eliminates the need to sign each transaction with a private key. This approach replaces ERC-2771 with meta-transactions. You can read more about it here. Pseudo-transactions provide abstraction over the user's account.