A complication I see is how to handle the case where a chromebook user wants to connect to the WiFi at a location where there's an interstitial they must accept (e.g. terms and conditions) before accessing the internet. This is the "captive portal" situation that was mentioned very early in in the thread. Let me clarify the importance, at least as I see it:
With HTTP (over port 80) the WiFi provider can easily redirect the user to the relevant "captive portal" page, because they are on the physical layer between the chromebook and the gstatic servers (and because HTTP is very trusting of the physical layer, allowing content injection).
On the contrary, with HTTPS (over port 443) the WiFi provider cannot successfully impersonate
gstatic.com, because it does not have the certificate of of
gstatic.com, so I'm not actually sure what it could do to get the client to the terms and conditions. Providing some arbitrary certificate would cause issues for the client laptop, because it would look like a different server than gstatic and the client should refuse the connection as unsafe. (this is working as intended, HTTPS is supposed to help prevent against snooping on the physical layer).
So, blocking port 80 on some chromebook would ultimately prevent that chromebook for accessing these sorts of WiFi points, unless I'm missing something.