A 4 way stop is unnecessary, simply requiring one direction to stop would work fine.
In New Zealand, with rural grid roads, they usually have 2 way stops (or give-way/yields) which will alternate, so you get priority at one intersection, then stop/give way at the next, and so on.
The article mentions a yield sign, right? I don't think that's enough. There needs to at least be a stop sign. Given the severity of the accidents, I don't think it's unreasonable to just go all out, especially if it really is a rural road with minimal traffic.
You're right. It's been a while since I've driven in the countryside, but I do remember a few of the intersections where visibility isn't so great due to trees etc. having stop signs.
Obviously, human error is a problem too, as the article states.
You should't be driving at 37 mph though an intersection with a yield sign in any case, which I guess is the whole point of the article and the suggestion to turn the intersection into two T-intersections.
In New Zealand, with rural grid roads, they usually have 2 way stops (or give-way/yields) which will alternate, so you get priority at one intersection, then stop/give way at the next, and so on.