“All seats of water closets provided for public use shall be of the open-front type.”
That’s how the open front toilet seat took off in the US, and in 1973 the International Association of Plumbing and Mechanical Officials (IAPMO) called for wider adoption of the U-shape seats.
Nobody’s forcing the world to make all public toilets like this but there are apparently some hygiene benefits that come with the shape.
Nobody wants to come into contact with a toilet seat that’s known the imprint of a thousand sweaty bums and is cleaned only sporadically, so the open front design helps you come into contact with as little of the seat as possible.

IAPMO bigshot Lynne Simnick told Slate in 2013 that the gap in the front was to allow women ‘to wipe the perineal area after using the water closet’ with the lowest chance of their hands touching the toilet seat.
As far as hygiene is concerned both men and women benefit from the missing chunk as it’s a portion of the seat that’s not going to get soaked in errant sprays of urine or splashback from the toilet bowl.
The gap lets women clean their bits more easily and removes the bit a man’s dingle would most likely brush against when raising or lowering himself from the loo.
Given that the oval shape is more popular in homes as it’s likely more comfortable there’s an expectation that you can keep your own damn toilet clean enough.