I have seen alternate greens employed for a variety of different reasons:
1. So that one or both of the greens could be quite small without the traffic wearing it down
(Pelican Hill, Shadow Creek, several other Tom Fazio courses, 10 at Riviera, all stemming from the 8th at Pine Valley)
2. To speed up play - using two parallel par-3 holes for alternate groups
(Several RTJ public courses)
3. To prevent women from having to make a forced carry
(Blackwolf Run)
4. As a compromise solution in restoration after the original green site had been abandoned
(#2 LACC)
5. Because the architect couldn't choose between two good options
(9th Pine Valley and 9th Pacific Dunes)
[EDIT - I forgot #6]
6. Similar to #1, in Japan, many older courses built two greens for EVERY hole in order to deal with turf problems common to Japan. Usually one green is bentgrass and one is korai, for winter and summer play ... but sometimes they are both the same grass, and they just use the "sub green" as a backup in case they have turf troubles maintaining the main green, due to the hot and humid conditions.
At Pacific Dunes the upper green came first, but after we did the clearing I thought a lot about the lower option ... there was a good site with a lot of natural contour, and I liked how it would cause players to want to do different things with their tee ball. So, I suggested to Mike that we use it as an alternate and combine that with alternate 10th tees, and he agreed. I don't think he would have let us build just the lower green because it had so much contour, but I convinced him it was ok if it would only be used part-time.