Mike---
Thanks ever so much for taking the time and trouble of posting the photos of your fabulous 1959 Bazooka Alan Ameche box. A king-sized gem.
For the gentleman who asked, Bazooka marketed a box containing a large number of individual one-cent twin chews of their wonderful bubble gum. These fit the category of penny candy, which existed at that time and was sold at small grocery stores, drug stores, and dime stores.
Topps wanted a way for kids to purchase more than a few pennies' worth of gum at one time, so they developed this type of box with 20-25 individual twin chews. I do not know exactly when Bazooka first issued a box of this design, but I am rather certain they wanted to increase sales of their product, and since they were already offering the regular wax packs and cello packs of trading cards, come 1959 they decided upon the perfect incentive to goose those sales of Bazooka gum---with a free prize baseball and then football card.
They were by no means punched off the box. As the others have said, they were purely hand cut cards, which caused all sorts of condition degradation on top of the other condition problems that arose from their manner of sale.
This is a great set, in every way.
As an aside, I am so glad Bazooka got the much better pose and natural happy expression of all-time great Johnny Unitas, rather than the looney-looking appearance Johnny gave the photographer for the other shot, chosen for the 1960 Topps.
---Brian Powell