Web Components are a very good solution if you're YouTube or Twitter and you want to let people embed your content while providing your own styling/behavior for it. It's basically a lower-overhead version of <iframe> that can set its own dimensions.
Web Components are probably also a good solution if you're a news site that serves 90% static text but occasionally wants to embed an interactive chart or something. It's basically a slightly more standardized, isolated version of the `<div id="chart"></div> <script>$("#chart").makeInteractive()</script>`-style code that sites like that normally use.
They might also work if you're trying to build a library of standard components (like "toggle switch" or "stepper control") to be used in apps written with a variety of different UI frameworks. Although this depends on good "cross-framework" support which hasn't really materialized yet.
Web Components might not be the best solution if you want to render your entire site in client-side JavaScript, SPA-style. But on the whole, there aren't many websites that want to do that—remember, 30% of the Internet is WordPress blogs!—and there are even fewer where it's actually a good idea.