Could we live without sports? Probably. Would we ever give up sports? Never. Not only are sports enjoyable (to most people), but they are also relatively good for your health. Many people stay in shape purely because of sports. Many people just need something to occupy themselves, in which sports fill that void. Sports also help stimulate the economy. Tickets and merchandise rake in the cash like you wouldn't believe.
As someone who plays sport regularly, I've learned that the health benefits are a huge part in the importance of sports. We'll start with some widely accepted views. First off, doing regular exercise helps your vital organs. Getting the heart pumping, the lungs working deeply and the legs or arm muscles working hard helps improve your strength and stamina. This in turn helps us fight other diseases more effectively and stay generally healthy. Also, if you play competitive sports regularly, you are more likely to develop a strong mental attitude that promotes persistence and hard work.
If you think about it, sports probably rakes far more money than many other industries. Everywhere you go, you see sports. Think about how much money is made off the merchandise of one all-star player. Now think about how many all-star players there are across all of sports. Don't forget about team merchandise; just because you don't have a favorite player, doesn't mean that Celtics hat doesn't look cool enough to buy it based on that alone. Ticket prices are outrageous, but people still sell out stadiums like it's nothing.
If sports were to randomly vanish from our society, I believe crime and unemployment would rocket upwards. The economy wouldn't know what hit it; Where did all that money go? At this point, a large portion of society depends on sports. We've had a taste and we're addicted, even infatuated. Never will we be without sports.