Opening Diversity vs Specific Knowledge

I have recently been showing some of my students some positions that come from very different openings, and am encouraging them to try out different systems. We've discussed various typical pawn structures, and central formations with typical plans surrounding them as well as natural development. The point is to play and study different openings so as to see and work through different sorts of positions.

The students I'm talking about have graduated from 1.e4 e5 systems and are looking at some Sicilian structures and some semi open games. Here are some typical positions to consider:

These are all typical opening positions that most experienced players will know of, but to kids, these positions are new and interesting. They have to consider strengths and weaknesses in the positions that they would not have considered during their play and study of 1.e4 e5 openings.

However, a question that arises to me is whether it is more important to play and study a diverse series of openings, or whether it is more important to deeply study a few openings. From a repertoire point of view, top players have tried both methods successfully, but for lesser players it is usually easier to play or learn a small repertoire which may expand over time. For kids, it is surely important to get them to examine as many types of position as possible, but at what stage should we be directing them to deeply study a repertoire?

Of course, getting the kids to work on their tactical, technical and positional understanding is vitally important, but opening choices are a fundamental question for all of us.

So I put the question to all readers of this blog: do you think opening diversification of specific opening knowledge is more important for an improving young player? And when, or if, does it change from one to one to the other?