I do feel that people over emphasise the impact that sport on terrestrial TV has on kids giving it a go. To a certain extent, I would question whether that was ever the case. Certainly I started playing rugby because that was the sport that my dad played, he took me to coaching to give it a try etc. Same with my little nephew. His dad liked cricket and rugby and so took him to those to give it a go. My nephew watches football all the time but has no interest in playing it other than the odd kick around.
You can then look at it in the context of the Open. Golf has 2 failings, it cannot be played in the street with your mates and it takes a high degree of commitment before you can even achieve some of the basics and even more time and effort before you can get out on a course. With the attention span of kids these days, you can show them golf on TV until you are blue in the face and it is just not going to click. Controversial I know but for most people I know, golf is something you take up when you can no longer play your preferred, more physically demanding sport and golf authorities would be as well targeting people 35 plus.
You then have the whole point of golf as a spectacle. At best, the drama is slow burning and you need time and a decent attention span to get anything out of watching it. Again, not something that is immediately attractive to kids. Kids also do not watch much terrestrial TV. Put it on youtube or Netflix and there may be more chance.
The coverage is also pretty mediocre when you compare it to developments for other sports. Whether you like it or not, football leads the way with graphics, camera work, everything to produce a bright and attractive package. What has golf added in the last decade, maybe shot tracer and that is it. We may like the pure experience of just watching the golf but kids don't. Hell, in this day and age, it is not even possible in many circumstances to follow one golfer round for the whole day on the red button or just watch coverage of one hole. With technology as it is, it really should be possible to make an event 'as live' being able to pick a viewing position, stay with it as long as you like, follow certain groups etc but golf just does not justify such innovation.
Then you have the issue of actually taking your interest in golf further. Kid sees the Open, quite likes it and asks if he/she can go and watch some golf, watch the people they have just seen on TV live. Sorry, not until next year pretty much. They all play in America and Dubai now.
What is my suggestion, bring back Grandstand on a Saturday afternoon. Do not focus it on football but show a wide and ever changing range of sports at all levels. I am sure that the rights would not break the bank. Through that I was as a kid given access to all sorts of sporting events with a chance to pick and choose what I wanted to participate in. If I did not like a sport, I still turned in the following week as something else would be on. It even works for golf as the coverage could be interspersed with other events so as there is no quiet time between shots etc.