If someone compromises the server itself there's basically no form of security from that point that would help. The attacker could just put anything on the downloads page, including a new checksum for the compromised download. Nothing is safe if the server falls into malicious hands, but TLS is much easier for both the user and the website host when compared to a checksum, so that's probably the best decision for this kind of system.

The only time where I'd recommend a checksum over TLS is when you're dealing with a very large download, like a Linux ISO or something. The TLS encryption would cause a noticeable slowdown, so in that case a checksum may provide the best user experience.