I'm doubting there's an add-on or anything (like a browser) you are looking for built into Kodi itself.
If you are dual-booting with Raspbian and Kodi, just boot into Raspbian and execute this command straight through LXTerminal to get the latest updates and the latest browser for Raspbian.
sudo apt-get update
sudo apt-get dist-upgrade
sudo apt-get install epiphany-browser
This browser loads HTML5 and shouldn't contain any flaws, as the RPI Company actually released this (RPI Website)
I hope this solves your problem you've been having.
I'm seeing where you are trying to go with this, since Kodi mostly lists items on applications and movie services which I find annoying also. If you can grab a Web Browser Add-on somewhere, that would probably be a lot easier. If you can't find one, this is probably your only option for now.
Just checked on my own Raspberry that you can use Chromium to use YouTube TV. The only issue I see with Chromium is the lag. I'm using a RPI2 Model B+ and I'm getting about 50% CPU Usage each time I open Chromium. If you still want to install Chromium, execute the following through your command line:
sudo dpkg -i chromium-codecs-ffmpeg-extra_45.0.2454.85–0ubuntu0.15.04.1.1181_armhf.deb chromium-browser_45.0.2454.85–0ubuntu0.15.04.1.1181_armhf.deb
Then, go to your File Explorer and run each .deb file with Package Installer. This should install each package for Chromium to your system.