To address your two points: The plugin is working perfectly on thousands of other sites so if it is not working on yours it is highly likely that the issue could be fixed had you posted on the support forum before leaving a one star review.
This was designed as a lightweight plugin. The first version I made for use on my own projects didn’t have any styles at all as I included the tab styles in the theme’s stylesheet. When I decided to release the plugin to the community for free I added a stylesheet with a set of styles that should look good in as many themes as possible. I included simple instructions to enable these styles to be prevented from loading for anyone using the plugin in the same way I was.
For anyone who is used to working with CSS, the default tabby stylesheet should work well as a starter set of tab styles which can be easily customised once copied into the theme’s stylesheet.
The customiser was introduced later as an optional add-on to enable people without CSS experience to style their tabs to match their theme. It was never intended to be part of the core plugin and is not essential.