There have been a lot of companies that tried the strategy you're suggesting; Friendster and Yahoo, for example. It turns out that "letting ... labor take such a big piece of the pie" is a much more profitable strategy.
This results from the underlying factor structure of the industry over the past quarter century. Classically, the factors of production are land, labor, and capital. Capital provides the means of production such as factories, bribed politicians, and lathes; land provides natural resources such as rainfall, sunlight, coal, and zinc ore; and labor applies one to the other to produce something which can be sold for revenue. This revenue is then divided up among the owners of land, labor, and capital.
The division doesn't reflect any kind of moral or objective valuation of the importance of the three factors; rather, it results from market processes in which the owners negotiate with one another.
Power in these negotiations results from owning a scarce resource. We're having this conversation with 100,000 other people on a web site hosted on a single server running on probably 200 watts. So the server costs maybe US$1000, the "land" costs probably US$1000/year, and it required labor that would have cost maybe US$100,000 to get it running in the first place, plus on the order of another US$100,000 a year to pay dang for moderation. The land and capital in this case are pretty fungible, and very little of them is needed. The labor is not.
A rank-and-file steelworker negotiating with the owner of a blast furnace is in a poor negotiating position because there aren't many blast furnaces around, he doesn't have one in his backyard, and there are lots of potential steelworkers with enough impulse control to avoid tripping and falling into the melt. The foreman who knows how to prevent breakouts from damaging the blast furnace and killing his coworkers is scarcer, but he's still probably limited to quitting to work for the other steel mill across town; he can't set up his own steel mill either.
By contrast, all the capital I need for my work is a US$300 laptop and a US$10/month VPS.
So the bizarre algorithm tests are not the cause of these salaries. The underlying factor structure is.
This also explains why hardware engineers are paid so much less than software engineers: an Intel chip designer can't quit and go into competition with Intel, the way the Intel founders and Chuck Peddle did, because even though you can buy foundry services on the open market, Intel's designs are festooned with patent barbed wire, and it commonly takes a million dollars and a year to get an ASIC fabbed, so you need significant startup capital. Modern patents are correctly analyzed as a way to improve the bargaining position of the owners of capital with respect to labor so that the revenues flow to investors instead of employees.
So why is it different in Europe and India? My guess is that you can't run a profitable business there without the right connections (not necessarily outright bribery), so people with the pull have the negotiating power, so they can take home the profits. And Europeans and Indians can't work in the US without visas, which are controlled by (capital-intensive) immigration lawyers and, of course, pull.