I'm really pleased I was forced to learn the web in layers. I learnt basic HTML, then CSS came along. I realised I needed some dynamic behaviour so looked into CGI/Perl and later PHP. The DHTML became all the rage and I picked up a bit of javascript. PHP began to show it's weaknesses and luckily Django and Rails popped up. Ajax became a thing somewhere in all that and returning JSON instead of HTML snippets was sometimes useful.
If you start now and dive into learning Angular/React/Ember/Whatever - you are so insulated from the lower layers it must get a bit baffling trying to understand how all the parts fit together and why some things are done the way they are.
tl;dr - Get off my lawn.
Dogfooding is nice, but not at the expense of risking not having the site showcasing your new autonomous vehicle company ready by the time the press release hits.