Plain CSS is very useful if all you have is an HTML page. Giving all buttons a consistent look is nice and easy if you can just specify that with a nice CSS selector. That's also the only place you can do it without changing all tags.
If you're building a component-based UI, that need is less, because all your buttons are created in a specific Button component. That's also an easy place to attach styling. You don't even need a separate file anymore.
But that's a wash. It gets much more interesting if you have components that are used in different contexts. Unordered lists for example can be an unordered list in the running text, but also a navigation list in the footer, the menu, or as tabs. There's some semantic logic to having those things as lists, but they usually look completely different.
You'd use classes and descendent selectors to deal with those differences. The downside is that those leak very easily to instances that you don't want them in. Having normal lists inside tabs inside running text requires careful engineering of the selectors.
The larger and older your project grows, the harder it becomes to get that exactly right in a future-proof way. At some point changing something for one item somewhere, can completely mess up something on another part of your site.
Inline styling, or Tailwind-style utility classes, are useful in that situation. Every component gets to be responsible for the way it looks and no longer has to care what anything else does. HTML tags that are used in different contexts will have their context right there, next to the styling. All part of the component.
The few remaining things that you need for consistency between components (colors, sizes, fonts, etc.) can be handled with CSS variables.