It's not. In the time it takes a jump-1 ship to move a load of cargo three parsecs (three jumps), a jump-3 ship moves three loads of cargo the same distance.
In this specific comparison, you are correct.
In practice, the next desirable world along a typical route could be 1, 2 or 3 parsecs away. So what happens when a J1, a J2 and a J3 ship all leave World A and travel 1 parsec to World B, then travel 3 parsecs to World C and then travel 2 parsecs to World D?
Ship J3 completes the route in the shortest time (about 6 weeks by standard reckoning), but suffers increased ship cost and reduced cargo for two of the three jumps.
Ship J2 completes the route in the a little more time (about 7 weeks by standard reckoning), but suffers increased ship cost and reduced cargo for some of the four jumps.
Ship J1 completes the route slowly (about 9 weeks by standard reckoning), but but has the lowest ship cost and highest cargo capacity.
I could run all of the numbers, but the results would apply to this sequence of jumps only ... another sequence will yield different results. My point is simply that the reality over the 50 week annual life of a typical trader will probably not be best represented by comparing a single J3 link to three J1 across the same link. The real issue is for a J1, J2 or J3 ship plying a given trade route, how many jumps will be less than optimal (1 parsec in a J3 ship) and how many will be optimal (2 parsec in a J2 ship) and which ship is best across the full range of the trade route.
I do not question your or Aramis' specific calculations as much as I find the focus of the analysis too narrow to automatically reflect the 'best' solution for the economy of a larger region. So I offer an alternative option for consideration.
If only two Jumps in 50 weeks of operation are J3 with an otherwise equal mix of J1 and J2, then suffering a loss in efficiency for three J2 rather than two J3 might be more economical over the long run.