No, a dishwasher does not need to be installed higher than the countertop. In fact, dishwashers are typically designed to fit under the countertop and are installed at the same level as the surrounding cabinets and countertop surface. This allows for a seamless look in the kitchen and provides a convenient loading height for the dishwasher.
When installing a dishwasher, it should be level with the base cabinets and the countertop to ensure proper alignment and functionality. The dishwasher's front panel should be flush with the cabinet doors when closed, maintaining a cohesive appearance in the kitchen design.
If a dishwasher were installed higher than the countertop, it would create an uneven and awkward visual effect, and it would also make it challenging to load and unload dishes comfortably.
So, to answer your question, the dishwasher should be installed at the same level as the countertop and surrounding cabinetry to ensure it operates correctly and integrates smoothly with the overall kitchen design.