Tanith I think your concern is the see-through element of it being glass. But if the glass is high enough then that is actually much safer than a wall or railings which may be shorter.
Think about it, children can climb on a wall or railings and there have been rare cases of children falling from balconies. But there is no way they can climb up a sheet of glass, so if the glass is higher than the child then that is very safe.
What is freaking you out is seeing a child apparently standing next to a sheer drop with nothing solid between them and the drop. But there is actually very strong glass there. It is an optical illusion in our brains that sees danger, because we are not used to seeing that. Maybe some people's brains register this more than others, which could explain why some people don't mind glass balconies.
I'm with you on seeing the perceived danger, but I think you'll get used to it. Go there and touch the glass, feel how strong it is and teach your brain to accept it!