You're absolutely right that Thunderbird – or any other application which gains access to the plaintext private key – could exfiltrate the key, make copies or take any other authorized action.
The solution is to keep the key on a smartcard (or any other suitable hardware) which performs all cryptographic operations itself and doesn't export the key. For example, there's the OpenPGP card, and some versions of the YubiKey also support OpenPGP functions. This way, Thunderbird can encrypt, decrypt, sign or verify mails using the smartcard, but it can never read the key.
If this is not an option, then the only way to deal with the risk is to carefully choose the programs that you allow access the your private key. Thunderbird is open-source and widely used, so it should be a relatively safe choice (assuming you've downloaded the correct file). But if you're dealing with more obscure applications, the only solution may be to not let them access the keys at all.
Note this problem isn't specific to PGP/GPG or private keys. As soon as an application can read sensitive data, there's a risk of misuse.