Yep, they were right on that count (even asthma would be tricky). Not only the people relying on meds, but very few people over, say, early 50s would have had much shot surviving the early die-off as well. Something like 15-40 would have been the sweet spot, and mostly in the middle of that curve. Add 15 years, and that should be the age of your population.
We should be seeing very few kids in the 15-20 old range right now. You'd have a few families here and there that made it, but it would be extremely difficult for young children to survive at that point. And they'd be an additional drain on the parents (extra food/supplies, having to carry them, having them cry at inopportune moments when hiding, etc), so it's likely either the child just wouldn't make it, or would eventually cause the whole family to die off. Having them forgo food to feed the child leaving them weaker when an attack comes, giving away position, tired from carrying them, diseases that the adults are innoculated against that the kids never got shots for, risky foraging mission to try and get them medicine, etc.
Not impossible, just think there'd be a couple of obviously-missing age bands at the start of this new world. And then there'd start being children in the 0-12 or so range as people started to settle in again, although in smaller numbers at first, so you'd expect that any children you see on this show would be quite young.