My believe is that they intend to fly hundreds of these. If you have 100 tethers from 0 to 60,000 ft or so, I believe that you would have many aircraft accidents. Recall that the British used tethered balloons to protect themselves from German air raids. There is no way that you could see those tethers while flying, until you were very close to them -- then it would be too late to avoid.
There are a dozen or so tethered balloons around the border of the US now, so far there have been no incidents that I know of -- but the border is a place where pilots are very observant. Also, the balloons are only at about 10,000 ft or so, so most planes are far higher.