I cannot replicate your experience so it’s hard to say. There could be caching you are unaware of. I’m assuming “no cacheing” means no WP caching plugin or proxy service like Cloudflare. Depending on server settings, your browser could still be caching pages. Be sure to flush your browser cache when checking. Some hosts cache pages on their end. If so, there ought to be a way to flush the cache of your content from your hosting account.
A long shot, you could try add_filter( 'show_admin_bar', '__return_false', PHP_INT_MAX );, which would override any other hooks that could be interfering.
Failing all of that, your theme or a plugin could be interfering. Try using the Twentytwenty theme and deactivating all plugins. Deactivate any must use plugins by renaming the /mu-plugins/ folder. Unchecking the option in your profile should now work. Restore your normal configuration, one module at a time to narrow down the cause of the problem.
