Contact bounce as you mention, yes, but also the board being connected will have filtering capacitors on the input that will draw a large current when connected to the backplane. In a server, for example, it's desirable that some maintenance is able to be performed without shutting the system down, hence the need for a device to permit connecting a board to an energized bus. By slowly ramping up the current into the board, a hot swap controller will prevent large inrush currents from flowing which could cause sparking and contact erosion or even disturb the supply bus from overcurrent/undervoltage.
Since some hot swap controllers use a sense resistor to provide current feedback on the ramp-up, it's easy for the manufacturer to add in useful features such as efuse capability, basic telemetry (e.g. current/voltage sensing), and an enable signal to turn on voltage regulators only when their supply capacitors are fully charged.