However, that doesn't seem to fit very well with the environments in which these systems developed... the parts of the Americas that the Three Sisters system developed in often had relatively abundant lands and scarce labor.

On what are you basing this assertion? The "Three Sisters" suite was developed in Mesoamerica, where it is often referred to as the "Mesoamerican Trinity." Beans and squash were domesticated during the Archaic Period (8,000-2,000 BC), and Maize was slowly domesticated over this period and achieved it's maximum yield by about 1,200 BC. Many of the regions where it was implemented, such as the Maya lowlands, had relatively infertile soil but abundant labor. Rainforest humus is only a few centimeters of fertile sediment on top of organically sterile loam. The three sisters combination was actually perfect for this situation, since maize is nitrogen leaching and beans are nitrogen fixing. Essentially, they compliment each other to minimize soil degradation. Since Mesoamerica had a high population density, labor wasn't really an issue.

As to why this agricultural suite is no longer practiced to day, I would point out that in fact it is still used in some indigenous communities. The fact that it isn't widespread is due to the fact that industrial agriculture typically requires monocropping. In the traditional three sisters system, beans and maize were planted together so that the bean plant would grow along the maize stalk. If you're planting and harvesting by hand, this doesn't pose much of a problem. In fact, it's probably easier since you have all of your crops in the same plot of land. A mechanical harvester, on the other hand, would have difficulty with this.

As far as the reasons behind why nobody in Early Modern Europe adopted the three sisters suite, I can't say. I would point out though that as Europe already had its own agricultural suite, it makes more intuitive sense for them to incorporate individual crops into their system than to adopt Native American agricultural technology wholesale.

One of the reasons why agriculture is not as vibrantly use in Native North America is because, as other answers have said, agriculture nowadays is done primarily in a mechanized way. Something that I do want to point out, and this is why I am writing this response is that, at least for indigenous communities in Mexico and Central America, agriculture is not longer a viable way for subsistence. With the coming of NAFTA (in 1994, so 21 year ago and therefore I am allowed to talked about this), agricultural products that were normally cultivated in these regions in traditional ways (like the three sister technique) were now introduced via international markets (especially from the number 1 producer of maize, the USA). In particular, cheap maize flooded Mexican markets to the point that it destabilized local maize production creating a situation in which indigenous maize could not longer compete in the national markets. Because of this many communities stopped the cultivation of maize and refocus their labor in other areas, massive immigration being one them. For example, in the Mixteca area of Oaxaca, there are indigenous communities that, while they used to produce maize for local consumption, nowadays they are basically becoming ghost towns where only women and children lived because the men have migrated, since agriculture could not longer be used as a way to sustain the population. So, while it is certainly being used by modern communities in Mexico and Central America, the three sister cultivation technique is in the decline.

There's a guy I always see whenever the "three sisters" system is mentioned who claims it is utter bullshit. He says they might have planted the plants mixed together, but the idea that they would actually grow on each other is nonsense..the beans would stifle the corn or be shaded by it, the wind would blow the whole thing over, etc.

But I'd like to get a second opinion on that. Wish I had a link to the comments...

my knowledge is more restricted to the agricultural side, some good points have already been mentioned, but I think I can add some smaller factors. for example the demand for specific cultural goods: maize is now widely cultivated in europe, but it is still mostly used as animalfeed. we have a saying in dutch 'what the farmer doesn't know he doesn't eat'. tomatoes and potatoes did catch on really well eventually, but early on there were a lot of suspicions/rumours about them being poisonous(because of their poisonois relatives). an extra reason for maize not replacing european grains would be pellagra, a deficiecncy for niacin humans. native americans used a process called nixtamalisation to prepare maize, wich prevents pellagra because it makes niacin available from the maize wich is present in a form not taken up by humans when untreated. this process wasn't exported together with the crops to europe.

also maize is a c4-plant, wich means it can tolerate drought better, but also has a higher temperature-optimum, therefor maize is planted relatively late(using it as animalfeed it can be harvested immature). in europe we already had established grains, including knowledge on how to prepare them, and our grains can tolerate cold better.

the three-sisters technique also requires a good timing of the sowing, I like gardening so I tried it myself one year, but since in my climate maize is planted out late, the beans have a shorter season, in my case the maizeplants did fine but the beans bore only 1 pod. so it would take a while before farmers in europe would've mastered this new technique, and if they already had a working system there would be uch incentive to put the effort in mastering this new method.

so what are the benefits we would've gotten by using the three sisters in europe? I think the main benefits lie in more efficient use of space, and the fixing of nitrogen by the beans. I don't really have extensive knowledge on the agricultural situation in all parts of europe at that time, but from my own country(the netherlands) I know that a lot of land is/was not suitable for farming because it's too wet. however, it's fine for growing grasses for cows to graze on, or make hay from for the winter. animal husbandry in general was common in that timeperiod(while the americas have less domesticated animalspecies), and all these animals produce shit. so getting nutrients(nitrogen being the most common deficient plant nutrient) would be less of a problem if you have plenty of animalshit.

crop rotation with fallow fields is also still widely used in europe, although I don't know how widely, but I know that if I see a field of maize somewhere, it is very uncommon to see that same field planted with maize again the next year. there are lots of benefits to crop rotation(as long as it's a good rotation), and when growing maize in a monoculture crop rotation would've been esential before the invention of chemical/synthetic fertilizers, because maize takes up a lot of nutrients from the soil. going by the benefits that the three sisters provide, I would expect the technique to especially flourish in a place where here is a serious lack of arable land, so that all land has to produce every year.