The recipient could keep their private key secure so that only their client could decrypt the messages, and take the risk of losing access to those messages if they lose their private key.
Or they could let their provider hold onto a copy of the private key so they don't ever have to worry about losing it, with the trade-off that the provider could decrypt their e-mails.
But either option requires zero user interaction on the sender's or recipient's part past "login and send" or "login and receive", while limiting decryption to the recipient and maybe their provider.