I don't think it's just an image problem but also that many parents these days molly-coddle their children and try to wrap them in cotton wool rather than let them experience life.
As an example, a friend of mine's son is at Uni studying Marine Biology. He was looking forward to his year's placement in either Vancouver or Japan. But, next year, these places are not available. Why? The Institutes in those countries couldn't fill the placements. Students didn't want to go and study for a year in a foreign country and/or the parents didn't want them to go. In my day (Geez, that makes me sound old!) the placements abroad would have been snapped up.
It's all about perceived risk - even the smallest incident with aviation makes the headlines, even when there is no real danger. Because events are more widely reported, society believes there to be an increased danger. I get criticised for walking alone at night. Crimes against women in those circumstances aren't on the increase statistically and are comparatively but when they happen, they are headlines. Young men are the most likely to get attacked at night but the percieved risk is not there because these events are not so widely reported.
I've been told off for not locking my door at night but, I am more likely to come to harm by having a fire in the house and in that case, I don't want to be scrabbling about for keys, I want to get out. The chances of anyone trying to get into the house (even if anyone knew it was there!) are remote.
The issue with aviation though would be responsible reporting and you ain't gonna get that from a journalist. They have a vested interest in selling papers or airtime and therefore will always make a sensational story out of a minor incident and they'll never let the facts get in the way of a good story.
As for the safety issue, are helicopter crashes more prevalent now than, say, 10/20/30 years ago? I don't know the answer but I suspect not.
Cheers
Whirls