...unless they inbreed (which a lot of european royalty did), in which case it works in reverse. Also, income mobility probably prevents this from having significant effects. According to [1] if your father is in the top pentile, you only have a 36% chance of remaining in the top pentile. Repeat this over 5 generations, and you only have a 0.6% chance of staying in the top pentile.
[1] https://www.brookings.edu/wp-content/uploads/2016/07/02_econ... page 4, table 1
IIRC this is a common misconception. The son of a traditionally handsome man isn't necessarily going to get all of the traditionally handsome male features from his dad; he might get some of his traditionally beautiful mother's traditionally beautiful female features. Genetics is a crapshoot like that.
Even if genetics are a crapshoot, I'd expect offspring of rich and powerful families to be, on average, more attractive than the median for their area from these environmental factors.
Honestly, that might be an advantage too. Humans think they’re good at these things, but this sort of judgement gives plenty of opportunity for more bias to creep in.
"Finally, it may be possible that a third variable affects the relationship of attractiveness and criminal accusations/activities. Socioeconomic status, ethnicity, and developmental advantages (e.g., nutrition, schooling) might be such factors.[29]"
Your physical attractiveness and the way you dress can both signal information about you. Rich & powerful men with status tend to marry attractive women, even if the men are not always attractive themselves. After a couple generations, rich & powerful families with status tend to have more attractive families. They can also afford better nutrition and educational opportunities. Dressing nice and fashionably indicates that you care about your appearance. While a few people can pull off the idea of someone being such a genius that they can't be bothered to care about their appearance, the general trend is that people that can't be bothered to care about their appearance also can't be bothered to care as much about other things, like preparing for work.
It would be nice if we could get rid of any attractiveness biases. I sure would be angry if I was disadvantaged in a court case because I'm not attractive. I would be extra angry if I was disadvantaged because my lawyer wasn't attractive. I have a feeling that just blindfolding the jurors or blocking their view would cause them to miss out on other important things like being able to see faces and reactions during testimony. At least if we know about the bias we can work to fight it in other ways. Getting people to "think slow" sounds like some Malcom Gladwell popular B.S. that has probably been debunked, but it's probably better than nothing, and any lawyer can probably work at getting juries to think a little harder.