Windmills on Power Towers?

Here’s a random thought.  Connecticut, where I live, has many tall towers with high tension electric lines.  They snake around the state and deliver power to everybody.  The towers here are just like those around the U.S. and in many countries.  They are built on wide right-of-ways with lots of space on either side of them.  They are over a hundred feet tall and are particularly ugly. Some folks think living too close to them is dangerous to your health; electro-magnetic waves etc.  (Studies have not proven a link between the big power lines and disease, yet.)

Most of these towers are in more rural parts of this area, and many are at quite an altitude.  Why don’t the power companies put windmills on some of these towers?  They could generate juice on already constructed towers, the power grid is literally attached, and since these damn things are ugly anyway, putting wind mills to generate more electricity on them seems logical.  The generation companies already own the land.  They own the towers.  There is usually lots of separation between the lines and any homes and businesses.  Looks to be perfect space to generate some cheaper, cleaner power.  As I said, just a random thought.  What do ya think?