Actually by the time of Reach, most of them are dead. They were trained (raised actually) to be disposable heroes, hence the secrecy of the Spartan III project versus the much more public Spartan IIs. Most of Alpha and Beta company were wholesale slaughtered on suicide missions deep in Covenant space. The only Spartan IIIs still left are the ones on Onyx, the ones selected to form Noble team, and head-hunters (deployed in pairs in Covenant space to... hunt heads).
Nothing wrong with being a good ol' marine, and getting your head torn off by a Brute, hooah.