Is there potential plugin incompatibility if theme has no header.php and footer.php?

I believe that it should be fine for themes to not have header.php or footer.php files. Block themes generally do not have these files. For example Twenty Twenty-Four, a theme built by the WordPress team.

If a plugin errors because a theme does not have the aforementioned files, then I would chalk it to some naivety in the way the plugin was coded and would avoid said plugin.

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