After about a week of troubleshooting the classic SharePoint Online blog subsite template (BLOG#0), I was FINALLY able to figure out why I could not edit the homepage.
There is a site feature called “Site Pages” that needs to be activated. Once activated, you can edit the blog homepage (assuming you have permissions).
Figure 1- Activate the Site Pages feature on your Blog Site in SharePoint Online. Now you can edit the blog homepage!
Figure 2- SharePoint Online Blog Site Edit button fixed
Figure 3- The SharePoint Online Classic Blog template is now editable for the homepage. The About this blog image can be removed.
I was lucky to run across this when troubleshooting why a modern SPFx extension would not show on a classic homepage.
Hope this helps!