The question of whether the child was properly denied entry into Schengen at FRA is speculation because OP lacks the details (and says so). But, that is really irrelevant to the question at hand.

1. It is always 100% the passenger's responsibility to have determined what documents are required and to have those in hand. If one does not know this information and does not know how to find it, one has to ask someone who does know. That is not different than most situations people confront in their every day lives.

2. Condor is subject to penalties for having transported a passenger and is responsible for returning her to her origin. However, Condor may recover those from the passenger, but it rarely occurs. In the moment, it is Condor's cost to bear.

3. There is little impetus to create a mechanism to fully automate TIMATIC because there are millions of permutations for most situations. It is far simpler to simply complete the interface regarding nationality, residency, stopovers, and the like and to read the output. Condor either did not bother or failed. That may cost Condor a good deal of money. But, that does not alleviate the burden on the passenger (or adult guardian).

In any event, given the ease of US passport renewals, it is tempting fate to attempt travel any time one is close to the passport's expiration. It can limit one's options in IRROPS and even more importantly, limit one's own ability to change an itinerary just because something pops up. A general rule of thumb would be to start the process at a year and then never have to worry.