This is Paris - not Kabul, not Johannesburg! Stop scare mongering! Agreed, you've been unlucky but this is not the experience of the vast majority of people.
The risk of something ranging between not very nicereally horrible happening is low. However there are additional risk factors to consider with a coach trip compared to an airplane ride.
Coach stations are not as well policed as airport, and in many cases in Europe, not as well as train station. As a result many of them can be a magnet for a more criminal or violent/impaired crowd. To that crowd people giving off a "tourist" vibe are what nectar is to bees. Young girls in particular would present as an easy mark.
My son speaks fluent Italian, and over my cold dead body will he be going near the London-Milan coach terminal at 15 years old unless in a big group or with an adult (or three). Day or night. I wouldn't go there willingly if I could avoid it. Despite speaking the language, despite knowing how to call the police and complain mightily, despite being a dab hand at running like the clappers and knowing the best direction to run in. Plus I can tell at first glance which cafè and shops to avoid even going in so I don't attract unwanted attention.
Everybody has to cut their teeth. An aeroplane trip would allow them to try out unaccompanied travel and find their sea legs as it were, in a relatively safe and controlled enviroment. A coach trip chucks up additional risks that has the small, but real, capsity to have their frist trip alone turn into something less than pleasant. It would be a pity if being so unprepared, so inexperienced left them wide open to a situation they were not well equiped to handle and left them reluctant to attempt a solo event again for a significant length of time. IMO it going by plane is like sticking on stabilizers the first time they get on a bike so they don't lose confidence thanks to the lowered risk of a nasty fall.
I think some people have this idea that Europe is all cuddly and safe. I've felt a lot less safe in certain places in Milan (including bus and coach stations) than I ever did wandering around BKK, especiallly since the eurocrisis hit and things started to get a bit less well policed and people a who were already not doing well, a tad more desperate.
Each to their own, it depends very much on the individual parent and child where the confort zone ends. But it would be outside of my own just based on how the situation today is casuing an increase in petty and not so crime, that is not always violence free, the decrease in visible policing due to cuts and the degree of inexperience of the traveller relative to the downsides of that particular mode of transport.