Are there any pitfalls pointing config sync to profile's config/install?
No, I don't think that is a good idea. default configuration is something else than the config sync folder. For example exported config has a UUID and system.site has a site UUID while default config shouldn't.

They are two different use cases. default config is for installing new sites and the config export is to deploy configuration between different installations of the same site.

What you might want to look into is https://www.drupal.org/project/config_installer, a simple installer that allows to install based on an config export/sync folder.