I’m not an automotive engineer, so I don’t have a great understanding of the benefits as perceived by auto manufacturers. Still, here are some benefits as I see it:

• Cheaper (fewer parts)
• More reliable (fewer moving parts, cables strained less frequently, fewer broken door handles)
• Recessed door handles are more aerodynamic (not necessarily an advantage of electronics)
• Remote door release (helps with frozen handles in the cold)
• Cool factor (helps sell cars)
• Flexible design (allows designers to do creative things with door handles/controls)