The drug store has bathroom scales with built-in bioimpedance devices for $50. Presumably good ones are somewhat more expensive, but since when is this "too expensive" for a test? A blood pressure monitor costs several times (to many, many times) that amount.

Bioimpedence is not very accurate. It is highly dependant on hydration and reads too high for anyone that has more than average muscle mass. The scales that you stand on are only measuring the fat in your legs so the reading is affected by the distribution of your fat. That being said it is a better alternative to BMI but still not great.

Bioimpedance might be a good (or not so good, I don't know much about it) tool clinically, but it would not work for epidemiological research, where the goal is to collect data from a large sample of people. So, most of these studies call people and ask for self-report. Almost everyone knows how tall they are and can give at least an educated guess on weight (whether they tell the truth is another story). In comparison, very few people have the device that you are talking about.

Every method of measurement has its problems. The key is to understand the flaws in your measurement tool and make adjustments accordingly.