Depends on what's your goal when using Tailwind. If you want to have clean templates, better stick with a traditional Bootstrap/Foundation -like CSS framework. If you aim for a small CSS bundle, perhaps Tailwind is an option (or PurgeCSS with some tweaking).
Agreed on those unreadable and almost unmaintainable HTML blocks, but that's better than div-itis on some templates.
About Tailwind UI, I just don't like UI frameworks, but that's me.