Shaun_DaBeast did a nice writeup in Dec '20 on how to get Zwift running on the Shield, here…
And I’ve added a bit more info a few posts later in the thread regarding using APKPure to install Zwift and manage updates, and using the Shield TV app to launch and navigate the Zwift app. It all actually makes Zwift very easy to live with on the Shield. I do wish for better supported graphics which the Shield could easily cope with but you don’t get through the Android app.
I too genuinely don’t get why Zwift don’t just support the Shield as they’re 98% of the way there already. Maybe it’s the additional setups that they can’t streamline - like turning on ANT+ FE-C support and writing the Android app to be controllable using the Shield Remote but at least they’re not actively hobbling us using Zwift on it so I’m not going to complain too vocally and the workarounds make it almost a native app.