I can’t speak to the totality of programs; regarding the majority that do not conduct speed work- there are many players who actually become slower.
Exceptions are players who also run track or who are fortunate enough to possess enough favorable genetic material to experience some improved speed as a result of, if nothing else, biological maturation.
I know someone who was on the coaching staff of a team that won the national championship in recent years and he said most players deteriorated in their physical preparation with each year due to the erroneous, heavily lactic, and overvolumized training program
Fortunate for those high level programs is that they’re deep enough with talent to overcome such coaching errors.