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.
Update:
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.
Update 2:
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:
wget https://launchpad.net/~canonical-chromium-builds/+archive/ubuntu/stage/+build/7916060/+files/chromium-browser_45.0.2454.85-0ubuntu0.15.04.1.1181_armhf.deb
wget https://launchpad.net/~canonical-chromium-builds/+archive/ubuntu/stage/+build/7916060/+files/chromium-codecs-ffmpeg-extra_45.0.2454.85-0ubuntu0.15.04.1.1181_armhf.deb
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.