Every Millionaire clone back then had to have some sort of qualifier round. Twenty-One had the audience vote for the contestant they wanted to see play next. Winning Lines had 49 people, 43 of which would be eliminated right off the bat. Even on Millionaire, 6-8 of the 10 contestants would leave with nothing but a few seconds of screen time and a free trip to New York.
The qualifier eventually fell out of fashion, but a 5/6 chance of getting on stage once you were cast was pretty generous, all things considered. The Terminator was on a whole 'nother level--a guaranteed $10,000 on a show where nothing is guaranteed, plus the chance at doubling your winnings? That's far too good an offer to pass up. IIRC only like 5 or 6 players ever opted not to use the Terminator. And to underline that cutthroat aspect, the show went out of their way to always refer to the contestants as a "team" working together, even though they were really all individuals technically out for themselves, and odds were very good that they would eventually eliminate each other.
That's another reason I think Greed, even it had been renewed, wouldn't have lasted too long--immediately after 9/11, there wasn't much of a public appetite for TV that was "cutthroat" or "vindictive". Weakest Link's ratings were in the toilet, The Mole and Survivor were postponed, and shows like "Temptation Island" and "The Runner" were dead on arrival. People were looking for feel-good escapism, and Greed wouldn't have fit.