You don't need to run your own server to use Let's Encrypt. You probably do want some sort of automated method for updating the cert due to the low expiration

You don't need to run your own server to use Let's Encrypt. You probably do want some sort of automated method for updating the cert due to the low expiration time (though it isn't mandatory), but that can be done in many ways such as a desktop application, or just having the shared hosting service add built-in support for Let's Encrypt, as Dreamhost has already done.