Should I rent $2M 7,500 sq ft house?

Hello,

I recently built $2M+ house in Alpharetta, GA area. The house is pretty big, approximately 7,500 with finished basement 6 br, 7 bath, 3 car garage, has sauna, 1 acre lot - farmhouse style. No pool yet, but can build one. 

Now wife complaints that the house is too big and wants smaller place, up to 4,000 square ft

I have low payment, approx $4,500 PITI, 2.625% mortgage, $640K balance.

I can afford to purchase another SFR but debating what to do with this one.

Should I rent it out? Not sure if local market supports long term tenants for $12,000- $15,000 monthly rent. 
I see regular 3-4 br homes are listed for rent at $3,000- $5,000

Some high end homes are listed for $15-$25K, but closer to Atlanta. 

What are your thoughts?

I hold a RE license so can save some money on the transaction cost. Don’t have much expertise on being a landlord.