Earlier quoted context omitted.
What's the problem with style attributes? I would use them instead of regular CSS if I could add pseudo-attributes and make them responsive. Since I can't I use Tailwind where that's possible.
Style attributes have very high specificity so they basically preclude using normal CSS files (they would mandate every line include !important)
They still cascade normally like CSS classes... see this example:
red text
red text
blue text
Ironically, it's actually complex CSS classes and long selectors that produce high specificity, which then requires even more specificity to override and eventually the dreaded !important