Because death was released into the world, all hope is denied, so being stuck in the box means there is not hope in the world.
Quite the opposite:
"Zeus gathered all the useful things together in a jar and put a lid on it. He then left the jar in human hands. But man had no self-control and he wanted to know what was in that jar, so he pushed the lid aside, letting those things go back to the abode of the gods. So all the good things flew away, soaring high above the earth, and Elpis (Hope) was the only thing left. When the lid was put back on the jar, Elpis (Hope) was kept inside. That is why Elpis (Hope) alone is still found among the people, promising that she will bestow on each of us the good things that have gone away."
Aesop, Fables 526 (from Babrius 58) (trans. Gibbs) (Greek fable C6th B.C.)
Your take may also be valid interpretation in that Aesop does make the point that Hope can now only promise good things that are gone from this world.
Redemption after death isn't really firmly entrenched until Christianity. (Pagan traditions tend to be pre-occupied with cycles of generation as opposed to Abrahamic religions which are focused on redemption.) In most pagan religions, there is only an underworld to which people go when they die, generally not nice places. The Elysian Fields are an early take on redemption after death, but entry is restricted to all but a very few, unquestionably out of reach of the average person, and even most heroes.
...according to Aesop, but Phil said: "Because Hope was stuck in the lid of the box, it was bloody useless, and false hope was the only hope humans had, because they are all going to die and dwell in Hades forever, and all the good things false hope promises are gone from the world."
However, I believe Aesop was presenting hope as a kind of balm. Yes, nearly all of us are going to hell, but the illusion of hope is the only thing that makes life bearable.
Indeed, Robert Graves, referencing Scholiast on Apollonius Rhodius (ii.1249) states that "Delusive Hope, however, whom Prometheus had also shut in the box, discouraged them by her lies from general suicide."
Of asphodel, that greeny flower, like a buttercup upon its branching stem- save that it’s green and wooden- I come, my sweet, to sing to you. We lived long together a life filled, if you will, with flowers. So that I was cheered when I came first to know that there were flowers also in hell."
-William Carlos Williams