The big problem I have with web components is that they aren't very useful. Everyone seems to think the component is the key to victory with modern web applications. It's true that it's sometimes valuable to have turn-key UI components, but they almost never stand completely on their own. They need to know about the rest of the application and what's happening - and this is where web components fall short.
Imagine a shopping cart indicator on an E-commerce site. (A so-called "mini cart"). These are ubiquitous. When a user adds something to the cart from other places on the page, the indicator (usually in the upper right corner of the page) increases the count displayed, and maybe adds a small picture/description to a dropdown list showing what's in the cart.
Components help with a vanishingly small portion of that interaction. Sure, they allow you to drop a single tag on the page and have the UI look the same. But how does the cart component know to update? Global event bus? Click event handlers? Polling? Callbacks? That mechanism is undefined with Web Components.
Communication between components is the key to winning the web application war, and this is why I think React has done so well. Their data flow/communication pattern with Redux is really understandable and easy to reason about. They've got first class support for passing application state around, and ensuring an action in one place on the page cascades to all places that care about it. To me that is infinitely more important for productivity than stamping out the same custom element over and over.