I'm not sure what sections of the American Air Mail Catalog 5th edition you are reading, but my sense from using it for a great many years is that most of the flights do have official cachets that were prepared by the post offices of the countries or in some cases by the airlines when the post offices were not able to prepare cachets. There are some sections where cachets are not illustrated or described and sometimes that is because no one has ever seen an actual example of the cover so the Catalog is not able to include an image or description. These first flight cachets are different from the privately produced cachets you see on First Day Covers where until more recent years the post office did not create cachets.
The reason why there are some first flights with small numbers of covers was not because of cachets, it was because there often was limited notice provided to dealers and collectors combined with the cost of airmail being significantly greater than regular mail and that combined with the weight limits on how much mail could be carried on those early aircraft. Famous flights typically have a great many covers flown but even then on all flights there was a limit to the weight that could be carried so you do not see numbers in the great many thousands like you see on many FDCs.
The survival rate of all First Flights declines every year as old collectors pass away or accidents happen. They even have been reduced back in the day such as a large percentage of the West Indian Aerial Express covers were destroyed in a hurricane that hit the home of the founder and first pilot of that pioneering airline, Basil Rowe, who had prepared a large percentage of the covers that he flew and was selling them from his home.
Prices for First Flights typically do better than comparable FDCs, but all stamps and covers of every kind are suffering from a declining number of collectors. I just watched an interesting
ebay sale of a large number of First Flight covers where the seller started pretty much everything at minimal prices of $1 to $3 and they all wound up selling with multiple bidders and most sold in the $8 to $20 range and a few sold in the $40 to $60 range. There are collectors and buyers out there for FFCs and the nicer ones go for substantial amounts, with the rarer and more desirable ones going in the hundreds to thousands of dollars.