Curl does verify certificates [1]. That does confirm that your connection is to the right server, but it does not confirm that the files were unmodified.
replySSL/TLS/HTTPS is more about encrypting the traffic and ensuring that there was no tampering with the file between you and the server. The steps that I describe are more about ensuring that there was no tampering between you and the original source. Those are two separate problems. If you just rely on HTTPS, somebody can replace the file on the server with a modified version, and you would not know.
But where do you get the checksum from? I realize in some cases you are downloading from a mirror (thus as long as you trust the source of the checksum, that is quite useful) - but if it is from the same host - then you are just comparing against the same webserver.
replyYou raise a good point. This is why people sign the checksums. The signature confirms that authenticity of the checksums. That somewhat moves the goalpost, though, since it then depends on where you got the source's public key, but it is still a more secure practice overall. The advantage of having the public key is that you only need to get it once and you can check many downloads later.
replyIt is also possible to have a signed file that you can use to check the authenticity of a downloaded file directly without having to use checksums. Rust [1] does it that way for its other installation methods.
[1] https://forge.rust-lang.org/infra/other-installation-methods...