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.