When you sell the same products in several WooCommerce stores, why should you sync stock between them?
The answer is obvious. When you auto sync stock across stores you will not have to update stock manually in any other stores where you sell the same products.
To update manually is a very boring and time-consuming activity. You rather want to spend that valuable time to promote your products on the net or improve your web store. Someone once told me that you can never improve a WooCommerce store too much, so your time is better spent there.