It would not solve the problem of cleaning if the u-bend wasn't visible, only lure the public into think a toilet was clean that probably wasn't.
Amsterdam airport has self-flushing toilet - they flush when you move away from them. This must ensure a basic level of cleanliness, as no-one forgets to flush.
You can get toilet seats that do not have edges that are hard to clean, and ones that can easily be removed from the bowl, so that you can clean under the back of the seat.
They are more expensive than the other kind,
Public toilets are cleaned generally speaking by cleaners who are badly paid, and whose supervisor has estimated how many minutes are needed to do any particular job. In order to pay the staff as little as possible (what the firm employing them calls a reasonable wage) you have to work fast.
Usually, however fast you work, you cannot do the job properly in the time alotted - I have cleaned offices and public toilets myself in the past.
To solve the problem of dirty public toilets, three things are necessary:
Installation of easy-to-clean toilets and hand-basins
Pay the staff for the amount of time it takes to do the job properly
Peruade the general public neither to wet the seatn or the floor, nor throw used towels and toilet paper onto the floor instead of disposing of these articles correctly.
If you implement the first two points, a great improvement will be seen. If it should ever become possible to get the public to use a public toilet with the care they extend to their own, then dirty public toilets will when all three of my points are implemented become a thing of the past.