There are three Ds: Dirty, Dull and Dangerous. Jobs that are any of those three are open to automation, meaning getting humans out of the loop. Thus, robots explore Mars, build our products over and over again, control the insides of nuclear power plants and keep track and dispose of terrorists. As the population of the Earth shrinks, the value of humans increases so the push to replace them grows also. Thus replicants.

Hunting replicants is down to be dirty and dangerous. Certainly this is a job you might want to get humans out of.

Assuming that Deckard is a replicant, it is possible that the programming for him ended where the movie starts: that he was activated and pushed out of a van downtown, decided to get noodles and is picked up by Gaff. It seems unlikely, though. Bryant seems very comfortable with Deckard, which sites to me that, replicant or no, Deckard had done this for quite some time.