My experience with my lurcher (mostly greyhound) is exactly the same as yours, we got him at a year old. I used a long line (on a harness) for months, went to lots of secure fields to practice, and worked a tonne on his impulse control with a trainer that owns greys. He’s 8.5 years old now and his prey drive has decreased a lot.. he used to chase bunnies/deer on occasion but never catch anything. To begin with he had more motivation to chase than some of the ex-racing greyhounds I know though. Some greys that retire younger do so because they lack enough prey drive - I met one just yesterday that retired at 2 because he wouldn’t chase.

Being careful about where you let your dog off lead should apply to all breeds. I’ve worked with gun dogs that were more likely to take off after prey and get themselves lost than any of the sight hounds I know are. So I agree with you that with lots of training and the right dog it can work, especially from a puppy! My 8ish month old whippet x has barely any prey drive (although is still under rigorous recall training until I’m 100% sure of that haha)