The concept of rapture in Matthew 24 is quite different than many Christians could imagine or accept.
That rapture is compared directly to Noah and the Ark where the wicked is removed from the face of the earth while the righteous few remains. Though not mentioned, it parallels the account of Sodom and Gomorrah where only the righteous few were spared and remained on the land while the wicked were exterminated.
The rest of the passages in Matthew speaks of the coming of Christ to take away the wicked (compared to that of a thief or as both judge and executioner to take away the wicked and cut to pieces).
After all, how could the meek inherit the Earth if they were taken away
The concept of a "New Earth" doesn't always mean we get transferred to a different planet. "New" can sometimes mean transformation or rebirth into a new creation like being born again (figuratively).
Obviously, if all the wicked people on Earth are taken out, the Earth would be transformed into paradise overnight. Poverty and crime would be eliminated because if all the righteous and meek people remain, no-one's greedy and selfish anymore and would share resources to everyone. With only few people remaining, there'd be over-abundance of resources for everyone.