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In a lake the size of Lake Michigan, it's doubtful that regulated sport angling would negatively affect the perch population. A relatively few spawners surviving the perch-jerkers can produce an abundant amount of perch fry to repopulate the lake. The rub is the conditions the newly hatched perch have to endure to grow into keeper sized and eventually jumbo sized.  If the number of jumbos drops off it's for two reasons. 1) Someone caught them. 2) They died from old age.  By far, the second reason is the most common. 

Actually, fisheries managers would prefer the jumbos get caught by recreational anglers. By the time they've reached 13 to 15 inches, they've probably spawned three or four times which (in ideal conditions) should result in a stable or even expanding population.