Let's assume that the total revenue (not profit) for a 4 year Olympics stretch is 4 billion US dollars. The article shows that the annual revenue is 1.375 billion, but we'll drop the 375 million dollars as expenses (and to make the math easier), and we'll consider a 4 year stretch since some years are going to be lower revenue than others.
Now let's say that they give 50% of that to athletes. That's 2 billion US dollars @ 500 million US dollars per year. Split between the 10,200 people, that you quoted above, gives about $200k per 4 years, or about $50k per year.
So no, cutting the salary of a handful of executives is not going to help, but that's not really the whole story.
Sure, your maths leaves $50k per athlete that actually competes in the Summer Olympics. But four years out, you're not certain who makes the team[1], so that money ends up split between the pool of athletes competing for each slot, which is quite a bit larger, particularly if your Olympic organization is trying to subsidise teenagers that might be the next generation of Olympians out of that same budget, and probably Winter Olympians as well[2]. So the idea that stipends to athletes might max out at $20k (as the article highlights for the US) starts to look quite reasonable even before we talk about the cost of sports coaches (lots of specialists and one-to-one coaching) and sports scientists, physios, masseurs, velodromes and other highly specialist venues, training camps, competitive trials, flights etc. On that basis, just as well that many national Olympic teams can top up their meagre Olympic allowances with sponsorship revenue, revenue from their own sporting events and government and lottery money.
[1]the ones you are sure will make the team barring serious injury are probably the ones most likely to have a decent sponsorship deal and not need the money so badly
[2]Not sure whether the Winter Olympians factor into the article's revenue numbers or what their competitor numbers are like, but they're surely even more expensive sports to properly train for...
I'm not sure the IOC should be responsible for any potential competitors vs actual competitors. Even if it's only limited to those actually competing in the games, and only given out after competing, then that's a lump sum of $200k which they weren't getting before.
As for the stipends given out by USOC for Team USA, those are specifically for the US, and there appears to be no information on how much of that stipend originates from the IOC as compared to sponsorships obtained by from the USOC directly. Even then, most countries do not pay stipends that come even close to $20k US dollars. In many places, if the athletes got a full $200k for participating in the games, it would set them up for a very long time (if not for life).
As for the cost of sports coaches, training locales, etc, there's a whole 50% of revenue left over specifically to help pay for those costs (on top of local OC's). As noted in the article, professional US-based organizations, such as the NFL, generally share 50% of the revenue with athletes. Those organizations also have many of the same types of costs, but still are able to maintain an approximate 50/50 ratio.
More to the point, "have you even looked at the economics?". Yes. The conclusion that I have is that there is huge gulf between, (and using the USOC specifically here), USOC's claimed 90% spending and the article's "6 percent in cash payments" to athletes. So it's not clear cut that direct benefits to athlete's couldn't be raised, and substantially.
If you deign to consider the possibility that providing the infrastructure and training to 10,200 people in dozens of sports in 200 countries on a 1bn annual budget might actually result in a higher level of overheads per competitor than training ~100 footballers at a single club with a $2bn annual budget, it becomes a bit more obvious why athletes get a smaller share of the pie in cash payments than participants in high profile team sports, even without the whole amateur ethos.
Funnily enough, a good friend of my brother's did spend 6-8 years of his life dedicating himself to getting ready for his first Olympics, going into debt in order to do so. Upon gaining a bronze medal he used the sponsorship windfall to cancel his debts and buy a house. I suspect if I suggested to him that the British Olympic team should have cut back on facilities or charged him for training and pushed him deeper into debt in order to ensure there was a moderate-sized lump sum waiting for him in the year he finally started being able to get money from commercial sources, I'd get a very weird look.
Now let's say that they give 50% of that to athletes. That's 2 billion US dollars @ 500 million US dollars per year. Split between the 10,200 people, that you quoted above, gives about $200k per 4 years, or about $50k per year.
So no, cutting the salary of a handful of executives is not going to help, but that's not really the whole story.