For example: Seconds left on the clock in a close game, Team A scores a basket, and Team B calls timeout. After the timeout, Team B throws in the ball from halfway up the court. What's the reasoning behind this? They just save like 2 or 3 valuable seconds by calling a timeout... It seems a little weird and unfair.
In basketball, why can a team calling a timeout inbound the ball at midcourt after the timeout (effectively gaining ground for free)?
According to Chuck Klosterman, it just always was a part of the NBA. (I don't believe it's a rule in most rule systems.)
Feel free to peruse this fantastic piece of journalism on the sadly defunct Grantland. He covers the topics of why it is thought to exist (to add excitement - things like Derek Fischer's Spur-Killing turnaround jumper, or even The Shot, probably happened because of this rule); but shows that it's been in the rules as far back as he can find rules.
I suspect it does exist because of the excitement factor, personally, and perhaps always has. But there's no evidence, as far as I can tell, and as far as Chuck Klosterman can tell, who's a much better expert (and writer!) than I.