Is it better to use mains power or an external power supply for a rack mount unit?
The main advantage is that by buying an off-the-shelf external power supply, you out-source all the safety certification to someone else.  Your appliance runs on safe extra low voltage.

A second advantage is that the appliance can be smaller and lighter (excluding the power supply).

The down-side for the customer is that they get a nice neat rack of equipment, and hiding behind it is a terrible mess of power supplies and cables.

It's also impossible to provide a proper power switch on the equipment itself.  The power supply will be plugged in and turned on whether it's needed or not.