Yes, these monuments were put up to honor Confederate leaders. But the timing of the monument building makes it pretty clear what the real motivation was: to physically symbolize white terror against blacks. They were mostly built during times when Southern whites were engaged in vicious campaigns of subjugation against blacks, and during those campaigns the message sent by a statue of Robert E. Lee in front of a courthouse was loud and clear.
No one should think that these statues were meant to be somber postbellum reminders of a brutal war. They were built much later, and most of them were explicitly created to accompany organized and violent efforts to subdue blacks and maintain white supremacy in the South. I wouldn't be surprised if even a lot of Southerners don't really understand this, but they should learn. There's a reason blacks consider these statues to be symbols of bigotry and terror. It's because they are.
When all those Confederate monuments and statues were erected: