This opens up an interesting discussion: what's the point of adding a sport to the program of the Pan Am Games?
In rhythmic gymnastics, Brazil has benefited greatly from the experience at the Pan Ams and has managed to qualify a group for many editions of the Olympics since 2000. Canada, the United States and quite possibly Mexico (in 2020) also managed to do so (or, in the case of Mexico, is expected to do so). The US almost qualified for an individual final in 2016 and is expected to do so in 2020.
What countries benefited from the experience at the Pan Ams in trampoline other than Canada and the US? None. Brazil, Mexico and Colombia won medals at the Pan Ams, but they are not even close to reaching a final at the World Championships (in individual trampoline) or the Olympics. Venezuela also won a medal in trampoline in 1955, but they never reached the finals at the World Championships (but to be fair the first WC in trampoline only happened in 1964). Argentina won a medal in tumbling in 1955 but never qualified for the tumbling finals at the World Championships (again, to be fair, tumbling was part of acrobatic gymnastics at the time and only had the first World Championships in 1974).