Why Not Store Encrypted Emails in Plaintext Locally?

Clients like Thunderbird are great because you have everything stored locally so you can easily search offline. They also support encrypting and decrypting emails in PGP. However, they seem to have the same limitation as protonmail where you can't search through encrypted emails.

I know that protonmail can't just store your key at their server since that would defeat the purpose, so the emails are all ciphertext to them right? But in Thunderbird, you already have the key and decrypt everything all the time. So why can't you skip the middleman in your local machine and store everything locally in plaintext? It's not less secure since if your local machine is compromised, your private key is also compromised.

Or at the very least give us the option and have a slightly less secure but much more convenient option.