Why is it so rare in the US to get kidney bean poisoning?

As the question you linked to says, canned beans are cooked thoroughly, so there's no issue. Pretty much the point of canned food is that it's ready to eat; if something required further cooking it would absolutely say on the label. (And given that people eat canned kidney beans without thorough extra cooking all the time, including in salads, clearly they're safe.) Ready-to-eat canned goods are presumably far more popular than anything else, so, most people aren't at risk at all.

It's also not a terribly likely issue with dried beans; it takes ten minutes at boiling to make them safe. Most people end up boiling when they cook beans, since it's usually easier to boil than it is to manage to hold a temperature below boiling that's still sufficient to cook. You have to deliberately get your stove to the right setting to hold below boiling, while if you err on the high side it'll boil. And seeing boiling liquid is a natural indicator of "this is cooking" that a lot of people will naively look for.

The main source of issues is slow cookers; warnings say not to use them at all, because they don't get hot enough, but in fact a lot of slow cookers do end up at a low boil anyway, so a slow cooker isn't actually a guarantee of poisoning even for someone unaware. (This isn't a guarantee, please don't try it!)

So kidney bean poisoning is a combination of several unlikely things: someone has to decide to cook dry beans themselves, they have to pick kidney beans over more popular varieties, they have to have not been warned, they have to have a slow cooker, it has to be one that doesn't end up boiling, and they have to decide to use it. Estimate what you like for the odds, but it's going to come out a lot lower than the 1/50 you guessed in your question.

As for how likely it is, the Bad Bug Book doesn't actually have specifics:

Reports of this syndrome in the United States are anecdotal and have not been formally published.

Several outbreaks have been associated with beans cooked in slow cookers (i.e., countertop appliances that cook foods at low temperatures for several hours) or in casseroles that had not reached an internal temperature high enough to destroy the glycoprotein lectin.

So it does happen, just not terribly frequently, and it may be underreported since the symptoms are pretty generic.

As Jefromi said, canned beans -- whether in the US or UK or probably just about anywhere -- are NOT going to contain this toxin, which will be destroyed with about 10 minutes of temperatures at a full boil (or up to 30 minutes near boiling, like the kind of "simmering" people tend to do with beans on the stovetop). The standard commercial canning process for almost all foods will require temperatures in that range for enough time to destroy the toxin.

In addition to the anecdotal stuff, you may want to check out this report, which is one of the few published papers on incidents like this. It mentions 50 reported incidents in the UK between 1976 and 1989, 32 of which it concludes are likely to have been actually caused by the beans. (A number of these also have confirmed laboratory tests for the beans, in addition to reports of symptoms that seem to point toward the beans as the source.)

This linked report recommends (as Jefromi says) at least 10 minutes of boiling, though it also recommends at least 5 hours of soaking for this specific type of beans.

As to why the US doesn't have more than anecdotal reports, again I agree with Jefromi that the symptoms are pretty generic (vomiting and diarrhea for several hours after consumption), generally followed by rapid recovery. It's not like a significant life-threatening illness. And unless people end up in the hospital, they're pretty unlikely to go and report incidents of random food poisoning to the CDC. That's part of the issue in trying to estimate incidents of Salmonella poisoning or whatever too: epidemiologists tend to estimate that only about 1 in 50 cases of Salmonella poisoning is reported. And Salmonella is a common food safety issue that could come from lots of different foods. With the present issue, there's only one food and specifically one variety, and it only concerns a less common product version (dry rather than canned), and it only happens in a small minority of recipe situations (mostly older or cheaper slow cookers). One last observation: cheap, small slow cookers are much less likely to be used in commercial situations than they are at home. This is likely another reason for sporadic reports -- the kind of food poisoning that tends to make the news tends to come from improper commercial preparation, which then will lead to an outbreak with dozens (or more) cases, which then tend to be investigated more thoroughly. That kind of mass event is quite unlikely to happen with this toxin.

I'd also speculate that the only reason they even got that many reports in the UK in the first place is due to publicity after an outbreak was reported in 1976, followed by a BBC report warning about these beans in 1981 (which asked for people to file reports of suspected incidents). You'll note that 2/3 of the reported incidents for that linked study come from the period 1976-1982.

Bottom line is that it's very likely this does happen to people, but if it's not serious enough to put them in the hospital and only happens to a couple people at home, they don't tend to file reports.