Eliminate cheap points, and nothing is cheaper and more demoralizing to a defense than giving up a point blank put-back shot off a missed shot.
The team that makes the most layups wins and offensive rebounds give you more layup opportunities. Offensive rebounds are often easily passed out to shooters on the opposite side for a wide-open-spot-up jumper.
Athletic Team vs. Non-athletic Team Rebounding
Sending two or three offensive players after your team's missed shot instead of getting back on defense is a luxury for athletic teams. However, if you are not an athletic team, focus on defensive transition to slow the opponent down enough to establish defensive position, dig in with your defense and rebound better.
End of Game Rebounds
It is much more likely that a team will have an opportunity to secure an offensive or defensive rebound during the last few seconds of a game. When a team is losing, a defensive rebound gives them one last shot at winning. When a team has the lead in the final moments of a game and they secure a rebound, they win.