In my opinion it is absolutely one of the most dangerous things you can do (or let your kids do).
But why is it so dangerous?
Life is unpredictable (I once had a tree fall out of nowhere while riding).
Horses are very large, instinctive, and reactive prey animals (even you're bombproof 30 year old).
If and when a horse spooks, not being able to move freely often adds to the intensity of the original spook because not only are they scared but are now unable to get away.
Physics. When a 1000lb animal suddenly hits a rope tied to something solid you are in a position to be; rolled over on/stomped in the frenzy, or be thrown head first into a tree, trailer, etc on the rebound if the rope doesn't break.
So the next time you consider getting on (or putting someone else on) a tied horse, remember that your horse needs you (to feed him) and you can't do that very well from the hospital bed or worse.