Being a close follower of Apple and their design decisions, I'd say a primary reason the Mac Mini doesn't have that connection is simple: it's not a portable computer, and it doesn't have a battery.
The idea behind the MagSafe connector is to prevent laptops from being yanked off tabletops when someone trips over the cord. When this happened before, the laptop inevitably ends up damaged. This, obviously, is a bad experience. As the MagSafe is a great solution to this problem, it was added to the laptop family.
The Mac mini is a desktop computer. While it is a very small form factor, and is easily portable, it still needs the "trappings" of a desktop computer to work – a monitor, mouse and a keyboard. So adding the MagSafe connector will only benefit the minority who takes this computer with them… And could very well tick off the majority if the MagSafe connector is pulled out in the middle of an important task (see the "no battery" comment, above).