Odd audio setup

I've started to work from home and take more official client calls from my home setup. I'd love to sound more professional, but not have a mic in frame. I like the idea of shotgun mics, but the movement is an issue.

Has anyone tried one of the new auto tracking gimbals made for cell phones with a shotgun mic on it? Is there a reason why this wouldn't work?

Sorry a little bit of a noob when it comes to audio setups.