1) only one pair of slip rings are required (to energise the rotating field coil) regardless of the number of phases produced by the alternator (three phases is common because of torque considerations).
2) The rotating coil can be supplied from a low voltage DC source and it is easier to use slip rings for this purpose than it would be to output a (typically) high output voltage if connected as a generator.
3) Insulation of the output is easier to achieve if the coils in which the emf is generated are stationary rather than rotating (as they would be if connected as a generator).
4) If permanent magnets can be used in the rotor then no electrical connection is required to the rotor and therefore no slip rings are needed at all. This is a major advantage from the point of view of system reliability.