Of course, your right :)
i've just added a checkup to the ThemeCustomizer which throws an error message with possible solutions (change chmod) as well as an additional faq entry.
Up to now i didn't thought that this was necesssary, but it seems that some hosting environments have configuration issues (they did not set the folder permissions correctly). This problem only affects a few users..
0777 is not a good idea (in case of security), therefore the plugin will not set the permissions automatically - but it's an acceptable solution for the cache-directory (maybe
0640 will also work, but it strongly depends on your hosting environment).
the new release will include these changes, thanks for your feedback!