One big reason it's a bad idea: The mizzen lives in the wind
shadow of the mainsail
direction indicated will always be significantly further forward than the "true" apparent wind. You will also find your indicated wind direction will vary with any change in mainsail
trim. This might not be a huge issue, unless you are going to use the instrument to feed wind data to an autopilot
, in which caser you'll find every sail trim change alters your course. That could be a real PITA.
It will also indicate lower wind speeds, being closer to sealevel, but that's not as big a deal.