The Kennedy Mint was a mass market, direct-mail coin dealer that advertised in general interest magazines for decades. It sold quite a number of "coins in a frame" - matching a group of coins to a pictorial theme (e.g., Lincoln Memorial Cents, Coins of World War II, etc.) and placing the grouping in a frame for display/hanging.
IIRC, they offered a variety of assembled coin sets in various cases (i.e., not just themed frames) and weren't bashful about the prices they charged. Its target audience was NOT the educated coin collector, but rather the casual collector or individual looking for a gift for a coin-collecting friend/relative. Its products were not good investments!
Though I can't point you to an advertisement for your specific
ASE set, it does seem to match the type of set the Kennedy Mint sold.
From what I understand, it closed its coin business about 10 years ago.
Collecting history one coin or medal at a time! (c) commems. All rights reserved.