Pre-merger, most players were taken in both the NFL and AFL draft and then chose which franchise they wanted to play for. As such, it was not all that uncommon for the Chiefs (and others) to draft a significant number of players who never played for their franchise. Some of those players would go on to be amongst the best of all time, like 16th round pick Roger Staubach, who went on to have a Hall of Fame career for the Dallas Cowboys.
In the context of the Chiefs’ 1964 draft class, the Staubach choice to play for the Cowboys is just salt in the wound for Kansas City. The team had 29 selections in the draft. Of those, 15 never played a game in the AFL. Of the 14 that did, only four ever played for Kansas City. Quarterback Pete Beathard was the best of those. He was with the Chiefs for just over three seasons and started 11 games for the team. Still, a first round quarterback who failed to start 40 games in the NFL and failed to throw for 9,000 yards in his career, even in that era, is not very good.
Defensive Tackle Ed Lothamer was actually with the team for eight seasons but only started in one of those. The Chiefs got two starts from offensive lineman Tony DiMidio and zero from defensive back Bud Abell. Unfortunately, the fact that the team got 27 starts from their 29 picks is actually pretty good compared to the rest of this list.