By tethering you may be making a "perceived" hazard into a "real" one! The only incidents with these items are caused by failure to follow the instructions.

Coastguard get called out - yes i'm sure it happens but only because users ignore the "Do not launch where the lantern could be confused as a distress signal" instruction.
So a beach launch is not sensible (unless of course you pre-notify the CG).
Setting fire to barns and hay bales - happens too, but only when these are launched in anything other than the stipulated calm conditions , and the idiot launching has not noticed the hay-barn 5 yards down-wind. What people fail to grasp is that these items, if they are still burning, are producing lift; it is only when they are out do they fall, harmlessly, back to earth.
Sad the kid was injured but IMO that splatter burn is consistent with the small child launching the lantern, short arms meant he was standing directly underneath it and no doubt looking up. As he let go, it tipped and the wax fell maybe 2- 3 feet (at most) onto his face. Why? Because parents ignored the warning "This is NOT a toy. For Adult use only. Keep children well away from lanterns at all times". To take blame from themselves the parents suggest it was "at least 40 feet in the air etc etc"
Our lanterns have been bio-degradable for quite a while...bamboo frame (our population of wild Pandas eat that ;-) ), tissue canopy, string support and paper/cloth wick (we don't use wax). So apart from a bit of debris that will dissipate in a short time, with no real environmental impact.
Back to safety
It is the person who launches, and where they launch, these lanterns that have the biggest impact on the safety. I mean, a golf ball hit straight down the fairway at 100mph by a pro is a harmless and enjoyable spectacle, but if a rank-amateur were to attempt the same feat in the middle of TESCO's car park on a Saturday morning then it will no doubt end in tears; But who is to blame? The golf ball or the golfer?

And finally, rocket sticks fall back to earth and can "potentially" cause damage,( as mentioned by an earlier poster) . Just as a matter of interest Re-enactor, to reduce the risk do you tether your rockets
