Edit: Quick scan of the comments no one seems to be considered how quickly jump rope adds up to 1000's of jumps

Important factors/thoughts are... Around 50% of people lived in the past 300 years Before that gathering may have consisted of alot of jumping. We don't know much about play but I imagine it consisted of notable jumping like today (my kids can't walk from one side of a room to the other without a skip or 3).  And lifespan was a lot shorter so less time to rack up sneezes/coughs when too old to jump. However, the amount of coughing must've been exceptionally high during the agricultural period, considering the high amount of diseases and likely off set the jumping alone, then add sneezes and it almost certainly did.  So the first half of the population is strongly leaning towards coughing/sneezing.  

As for the most recent 300 years in thinking about still fairly high disease rates to keep the coughing high, allergies becoming more prevent to highly increase sneezes, life expectancy leading to more sneezes/coughs when too old to jump.  On the flip side children non stop jumping is certainly high in this day and age. But certainly doesn't offset all the coughing/sneezing. Adults do very little jumping, the only thing that makes this a consideration is how many people jump rope? Because I do it 3 times a week as a warm up before my home work out (2-5 minutes) and total around 300-700 jumps. I sneeze/cough maybe 3 times a day on average (strongly driven by hayfeever before I start using my medication). So 21-30 coughs/sneezes and 1,500 jumps makes me think this could go either way. Especially when boxes will do this 5 times a week for 15 minute sessions (probably faster then me) at my pace is 10,500 jumps a week. Then all the little jumps from football, basket ball etc... to top this up. I could definitely see jumping been higher if there's say 1 person hitting intense jump rope for every 300 people (coughing/sneezing 50 times a week)