Ok, I feel very qualified to chime in on this since I competed in track and field for nearly 10 years.
My personal bests:
22' 6" long jump (but this is with a 56' "approach")
5' 8" high jump (not great, but I am only 5' 7" myself, so I was always proud of it)
11.5 100-m sprint (again, not great, but pretty decent)
4 min. 23 sec. mile (again, not great but good IMO)
A "triple jump" is three "jumps" in a row, so not really useful in D&D unless you are literally hopping, skipping, and jumping over a creek or something.
The idea of long jumping with only a 10-20' approach is very limiting. You just can't get up to speed that well quickly enough to jump the 20+ feet many people think about.
For such a short approach, the simple passive system actually works pretty well IMO. My STR during the years of competing would have been a 12 probably, and with the minimum 10' approach required in RAW my "jump" would really have been a "stride or leap", and getting 12 feet would have been pretty easy.
To increase jump distances, I would allow a DC 10 STR (Athletics) check. If you succeed, you add your proficiency bonus to the distance. My proficiency in Athletics would have been maybe a +3 (I was good, won some events, etc, but hardly top collegiate or anything, and no where near professional). This would allow me to make a 15-foot "jump" with only a 10-foot approach, and I could see that happening back in the day.
Other options on a successful check would be:
Adding your STR modifier
Doubling the approach (so you can really "run" into the jump) could either lower the DC or double the proficiency bonus.
Double modifier/ proficiency for encumbrance less than STR (so 10 lbs or less for STR 10).
A final note: competitive jumping in school and sports lands in the "pit", a sand-filled landing zone and many jumpers land "near-prone", throwing themselves forward. Landing on a hard surface and on your feet, would drastically reduce the distance you could jump. Also, you aren't wearing a lot when you jump competitively, in D&D having traveling clothes, armor, and gear/weapons would severely hamper your jump.
That is why I think of jumps in D&D more like "leaps" or "strides".