No, boards don't hit back.
But there's a reason you do use them. Bruce Lee also did a lot of practicing with boards.
Breaking a lot of the time shows you what's wrong with your technique. The mechanics required for speed, precision, and power. For instance, a side kick is not the fastest kick around, but one of the most powerful (to me, it's my most powerful kick). Power breaking does show a great deal of things. Special breaks that require a special method of holding are required for things such as speed breaking. One of the hardest methods is having someone drop a board and you having to break it in midair. Now that's a combination of speed, power, and precision right there.
But breaking is never the fundamental goal in any combat or sport art.
It can relate to weapons. You can spar with a bokken or a shinai all you want, but you're going to have to cut sooner or later. If you don't, and you're blade alignment is a bit off among other things... Or with firearms. You have to go to the range and hit some paper targets. Yeah, they don't move, nor do they shoot back, and you aren't moving either, but one obviously understands the benefits.
Is breaking required? No. Are they helpful? IMO, extremely.