If they had done this they would be accused of ethnic cleansing as well as genocide. the negev isn't an altogether welcoming place, any death natural or otherwise that happened there would be blamed on the jews as proof and it would be an even bigger PR disaster. Egypt and the sinai would have a similar problem. Even Trump's recent suggestion of temporary resettlement to a populated area has been met with calls of ethnic cleansing and genocide. Most of the supposed supporters of the palestinian people don't care so much about their fate so much as they hate Jews and love the easy cudgel they make for attacking jews.
Putting that aside, no one, not Hamas, not the Israeli public, not Netanyahu, and certainly not the IDF, not any neighboring countries, not the wider world believed the war would drag on this long. Everyone thought it would be over fairly soon. Hamas probably didn't think there would be a war because israel itself was on the brink of a civil war, the Israeli public with their strong belief in their military might thought the war would be over before the new year and the IDF and politicians (BN included) likely had a similar belief, that A) Hamas didn't have an apatite for a long war, and B) the IDF would be able to quickly return the hostages. Everyone else also believed in the might of a stronger more organized force against a much weaker force that supposedly also had to care for their own people.
Instead Hamas showed they had no concern for their own people, and they had significantly deeper fortifications than the israeli security establishment knew about. So here we are almost two years later, and no end in sight.
Still it would be better for civilians even if not any better from PR standpoint. Also with some of the civilians filtered out Israel might have easier time acting boldly against Hamas in Gaza.
Putting that aside, no one, not Hamas, not the Israeli public, not Netanyahu, and certainly not the IDF, not any neighboring countries, not the wider world believed the war would drag on this long. Everyone thought it would be over fairly soon. Hamas probably didn't think there would be a war because israel itself was on the brink of a civil war, the Israeli public with their strong belief in their military might thought the war would be over before the new year and the IDF and politicians (BN included) likely had a similar belief, that A) Hamas didn't have an apatite for a long war, and B) the IDF would be able to quickly return the hostages. Everyone else also believed in the might of a stronger more organized force against a much weaker force that supposedly also had to care for their own people.
Instead Hamas showed they had no concern for their own people, and they had significantly deeper fortifications than the israeli security establishment knew about. So here we are almost two years later, and no end in sight.