There is much more to securing a server than just blocking a few ports. Typically on a server, you implement a "default deny" policy that blocks traffic to all ports and then you exempt only the specific ports that you need. So if you don't need ports 80 and 443, then by all means, they should be blocked.
You are most likely correct in saying that there are no known vulnerabilities directly against port 80. What you need to ask yourself is whether or not there are any vulnerabilities in whatever application is listening on those ports. That is where security issues happen 99.9% of the time.
It sounds like your aim is to force users of your application to only use the HTTPS channel via port 443. Rather than outright blocking port 80, I would highly suggest opening that port up and just doing a redirect to HTTPS for any clients that connect there. That way, users can type in "example.com" in their browser, and they automatically get redirected to "https://example.com". This is not a necessity, but it is generally a good practice to improve UX.