Life can't be the "greatest good," otherwise, death would conversely be the "greatest bad." And death is nothing to us.
Pleasure (i.e., living a pleasurable life) is the goal, telos, beginning, and end.
I think that is another perspective issue. Being dead is nothing to us, but losing our lives prematurely before it is necessary is a huge thing to be avoided (that gets us into the issue of how long should we seek to live.) That's a huge issue that deserves its own discussion. It is NOT a matter of indifference to me if I die tomorrow vs 20 years from now which I might reasonably hope to do given state of health, etc. So that "Death is nothing to us" line is something else that has to be parsed VERY carefully.
So I think that we have a big issue here about being very careful about defining what we mean by the "greatest good" -- and I think we have several texts that warn about that exact issue, including the Plutarch "walking around talking about...." text.