Recessed areas are good at keeping water in a contained space but an inverted glass or cup will skate on the water trapped inside it. Some customers with this type of drainer use a tea towel to stand their washing up on when not entertaining. A waterfall front edge profile to a wet area can help retain splashes and prevent water from dripping on to the cabinets below.
We can make any style of drainer that you would care to draw but have shown the common ones here.
It is important to remember that water will never just run to the plug hole automatically. Surface tension means that some water will always remain in drainer grooves and sit on top of recessed areas.