The Austrian school does not dominate academia, not even close. Even the Wikipedia article you linked to says it's a heterodox school, meaning it's not mainstream.
I used Lit components in a large FE project, enjoyed doing so and am happy with my choice. I don't use the shadow DOM at all.
The project is Converse.js, an XMPP chat client. It's an old project that was originally created back in 2013 with Backbone.js.
I first replaced all templates with `lit-html` when I first heard about that, and then when lit-element (and now "lit") came out, I started rewriting the project to use that.
This app has since been integrated into many different websites that rely on other frameworks like React and the fact that Converse.js is a web component (<converse-root />) makes this easier.
Your website is very clever, I like it, but unfortunately Google has classified it as a dangerous site with a phishing risk, which I think is understandable because you're effectively pretending to be Google.
Also, is it really a defense department when you're starting wars of aggression every 15 years or so?