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.
Actually, no. There's no need or possibility to make it "cleaner", but there's always the direction of making it more "high level". These are very different things.
The platform APIs are not opinionated about templating, they just provide proper mechanisms for declaring elements and having isolated DOM subtrees. It makes sense to leave templating to libraries, because… well, good luck on getting even just two people to agree about how templating should be done :)