YSK: Cats don't like their whiskers touching their food bowl. This is why they beg even if food is still left at the bottom.
Whisker fatigue causes stress and overstimulates their senses. Using a flat bowl or plate will relieve this issue and allow your cat to eat all their food without stress.
You can also search for "whisker fatigue" bowls specifically made for cats.
Tell that to my cat who does anything and everything in her power to drink out of mugs and half full glasses when she has a nice wide fountain full of fresh, clean, filtered water 5 feet away.
When my cat was a tiny kitten learning to drink from a bowl he would always dip his face in too far and get a nose full of water, causing him to sneeze. He learned to always dip his paw in the water first to see where the surface is before putting his face in. He still does it every single time. It's pretty cute.