... Such solution would have a number of advantages.
Such as?
I can think of a lot of disadvantages, such as slower interface response times, exposing your interface to anyone who connects to a port, debugging it in all the browsers and their different versions, interfering browser plugins and adblocks, phishing, etc. The GUI is very simple, you won't get much advantage by using a browser as your GUI, it will probably be more difficult.
I am all in favor of UI / backend split, but see no advantage in making main UI browser-based.