I think this masks a lot of complexity that you have to manage when taking on this approach. And it's not because the approach is good or bad, more what it is or isn't suited for.
The example on the homepage is very slickly presented, but the end result markup is extremely verbose. If I have a Card component, I would like to update them all at once when needed which is what css classes are generally good for. I find BEM naming conventions much more friendly to come back to than markup full of miniature class names.
Yes, you may have more than one card in your system, but in all likelihood you aren't repeating the HTML for that card more than once, rather you have it in a template of some kind which is called. So while you may have more than one card on your site, you probably don't have the template for it defined more than once. (at least ideally you don't)
For those cases where you do want to extract that code, Tailwind makes that easy to do.
Tailwind is a weird thing and like I said I really thought it was insane at first. But after rewriting a site in it in a few days I have to say it is better than the standard semantic CSS by a mile.
Though, you can still use BEM with TailwindCSS through the @apply directive. Adam calls the directive a kind of "trick" to get more devs on board with utility-first but it does help a lot of you're used to reasoning about CSS with BEM.
I will stick to BEM + colors and sizes maps because this feels almost like using the style tag on each element.
For non-css expert engineers writing spa components, tailwind can be useful.
I can also see that it’s not trivial to mix tailwindcss and scss processors so it’s a no for me.
It has the benefit to limit spacing and color sets to presets but I already do this in my BEM codebase.
Then you update the styles of the card again but the new styles clash with the ones in those tailwind classes and you end with broken styles in some elements.
Mixing components and utility classes is a recipe for future chaos.
edit: thinking more, you can override classes. So yeah, maybe utility/atomic classes are not as effective here.
Or, if it is a minor change, then conditionally include / exclude a small subset of tailwind classes.
The point is to not write your own CSS, you only use tailwind classes. In this way you can look at the template for each of your components and reason about / edit their style and layout easily.
It also makes responsive styling a lot easier in my experience.