Does whomever wrote the question have any idea how a toilet really works? The level of the bowl after flushing is what overflows the trap and flushes the toilet. As drawn the level of the bowl would overflow the trap and drain the bowl until the water was below the bottom of the top portion of the trap resulting in almost dry bowl. If it had a flush handle the absence of water in the tank would cause the bulb to drop and water to begin to refill the tank. Given the size of the tank in the picture it would never refill the bowl.
If you are trying to get people to think broadly all aspects of the question and any attached picture/drawing should correctly reflect what you are trying to prove.
Yes a large amount of water head would have the affect of being able to push a bigger amount of waste but not in the toilet as drawn because that water would be gone over the trap.
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Look at these two images, and you will see.
http://www.smarterflush.com/universal/toilet-bowl.gif https://i.stack.imgur.com/KaS7a.jpg
It all has to do with pressure and gravity. Higher water has a higher potential energy. It's water that pushes water.
Uh... a toilet works by you doing your business not it, flushing it and maybe put a fragrance thingy into it