If encryption is breakable with a large amount of effort, then it does several useful things:
* It prevents people without the resources from accessing your mail.
* It may provide short-term security, which may be sufficient.
* It makes those who do have the resources be selective in whose encryption they break.
For example, if it takes a minimum of a week to break the encryption on an encrypted web connection that discusses an embargoed news item that will be published in 6 days, that's good enough.
Another example: If a government wants to crack down on encrypted communications among drug traffickers, but it costs them $10,000,000 for each decryption effort, they will need to pick and choose who they go after.
There are encryption systems that are provably unbreakable without a key, such as a one-time pad. Unfortunately, they are usually not practical to implement correctly.