Well, forget about "Polymer the library", it served us well but it's very legacy at this point. The successor is https://lit-element.polymer-project.org and it's awesome.
Why on earth do you need something that heavy? How about this 200-line lib instead: https://github.com/wisercoder/uibuilder It lets you TSX format (same to React) to implement as well as to use web components.
Huh? lit-html uses standard JavaScript. That's it. JSX is a non-standard extension. So yes it is more standard than a non-standard, and lit-html runs directly in browsers without any transpilation while JSX very much doesn't.
VS Code is as able to analyze lit-html templates as well as JSX via the lit-plugin extensions. It gives you type-checking, code completion, hover-over docs, and linting.
Yes, JSX needs transpilation but that happens at compile-time. Which is better, pre-processing at compile-time, or "transpilation" (i.e., string processing) at run-time?
OK, so plugins can enhance code editing. But what about compile-time checks? With TSX, if you have a mis-matched tag the TypeScript compiler will give you an error.