As someone who has kept horses for many years I can see lots of issues with tethered horses.
A horse left on a long tether is at risk of getting the tether tangled around its legs, leading to panic and a fair chance of a broken leg. Often horses are tethered by a main road where they are especially likely to be spooked.
A tethered horse is open to attack by hooligans, and being tethered it can't escape .
Speaking from experience ,the public have no idea about handling horses. Both adults and children will attempt to approach a horse from all sides often moving quickly and shreeking. A frightened horse is quite likely to kick out and cause serious injury, possibly death ,especially to a child. A tethered horse is unsupervised, and therefore the public can't be warned.
No one who cares about a horse would leave it tethered, and a danger to itself and others.
Some horses need to be protected from their owners!