As Obsidian app themes become increasingly full-featured to support many plugins and app features, I believe that the official documentation should no longer recommend to users that app themes can be used for Publish sites.
Some Obsidian themes have grown to multiple megabytes because fonts and icons are being URI encoded in the CSS. This means that every user who is loading an Obsidian Publish site is downloading styles and fonts for the entire desktop app. This reduces performance of Obsidian Publish sites, and leads to a worse user experience.
As an example, I have been rewriting Minimal theme for Publish. The app theme is currently at 353 KB whereas the Publish version is 17 KB.
Developers should be encouraged to create Publish-specific themes that would be available to users as a separate resource. This could be a publish.css file stored in the same repo as the main obsidian.css file for the theme. Alternatively Publish themes could have their own separate section in the Community Themes.