Open ended seats and "hovering"
I, too have wondered about the open front seat. As it happens, an additonal function they serve when installed in a well designed outhouse or "Dry" Urine Diverting Toilet is to allow a small aperture for clean air to be sucked down the toilet riser by the pressure created by air moving through the larger diameter vent pipe. But I realize this is a forum on toilets that employ water.
More suprising and frankly, disheartening, is the apparent prevalence of "hovering" in public toilets by women, either straddling the bowl or standing on the seat or bowl rim in order to avoid contact with the seat. This obviously makes for more mess in public restrooms which only increases the degree to which the next people treat the facility with disregard and encourages further "hovering".
I learned about "hovering" when interviewing a college student who was a member of Engineers without Borders, and we were discussing the challenges they faced installing rural sanitation in Africa. She confessed that she and every woman she knew "hovered". When pressed, and mind you, this is a senior in college studying in science, she said she was concerned about STD's. Some notions die hard.