Apparently the u-shape is intended to allow women to wipe without touching the seat, and maybe also reduce male contact with the front. But you have to take a bunch of people's word (which I suspect to be guesses) for that.
[1] and I've been on standards committees where people are trying to imagine what the previous generation were trying to say, since standards usually only tell you what, and are short on the why.
Most "commercial toilets" are designed to be easy to clean and run off of "mains" pressure - commercial buildings have enough flow that they can flush directly without storing a buffer in a tank. And many commercial businesses have normal "home" toilets, at least around here.
> This is an open-front toilet seat, and thanks to the American Standard National Plumbing Code, it’s the go-to for most public restrooms. This code was created in 1955 and further cemented by the Uniform Plumbing Code in 1973 by the International Association of Plumbing and Mechanical Officials (IAPMO).
You can follow the links in the article I linked, or do a bit more Googling.
It's not a single uniform law, but a code that then got (and gets) adopted by lots of localities using different legal mechanisms. See https://en.wikipedia.org/wiki/Uniform_Plumbing_Code
There's a lot more laws and regulations for the 'commercial' toilets. Eg the U-shaped open seat is mandatory for public toilets in many places in the US. It's not a choice they make for commercial considerations.
Btw, 'commercial' toilet is a bit of a misnomer: it's against the law to run a toilet business in most of the US. (Specifically paid toilets are outlawed.)