To do what ? the video have lags and the quality is horrible.
Instead if you want it just for remote control functionalities, it a waste of hardware resources have a video streaming always active on your phone. Since you should also press very small buttons is also inconvenient. You can control every multi touch apps and games in better way without waste hardware resources of you phone and battery and with more confortable buttons or with the mouse and multi touch gestures on touchpad.
Instead, if you need it for remote support, is another story, and can be just sufficient. But how many people do remote support for others ?
What do you do with Teamviewer ?
Teamviewer is a VERY useful tool. On my old Android box I used it to run maintenance on it while my girlfriend was watching cable in the Living Room. That way, I could run maintenance or test the box w/out bothering her while she is using the cable box connected to the same TV.
I have not tried this w/ the Nvidia Shield TV yet b/c I have an HDMI split to another monitor in my office as well as a chromecast in my office that I can simply just cast my Shield TV to. This allows me to run maintenance on my ShieldTV w/out disturbing my gf in the Living Room. Also, video streaming is never "always active" b/c I can automate connection/disconnection very easily by sending messages to enable remote sharing via Join or Pushbullet.
That said, I'm sure I'll find a reason to want to use TeamViewer eventually.
I run a security system with my Shield so if I am away from home and need to access the Shield for any reason, TeamViewer is my only option.
I've never tried to use TeamViewer from an Android Phone, however. Didn't think it was possible. If so, than that's awesome!