First - most of them have little real historical value,
having been put up in two major waves. The first, roughly around 1900, were the same time as the worst period of race relations in general, and the onset of racial terrorism and oppressive laws. The second, in response to the Civil Rights movement of the 1950s and 1960s, basically an angry response to the push for equality. In other words, they aren't monuments to history, but monuments to oppression. This is why many of them are sitting outside courthouses and government seats - much like many school that were supposedly integrated had their names changed to Confederate leaders in the 1960s.
Second, many of these statues were mass-produced, and rather cheaply at that, so they have little real artistic value.
Third, as we've seen in Charlottesville, they serve as modern-day rallying points for white nationalists, Nazi fetishists, Klansmen, and other such terrorists. In other words, they're public nuisances.
Fourth, most of these monuments, when they reference history at all, actually reference the "Lost Cause", a historical fiction of the poor downtrodden South that simply wanted to have their own rights but were ground by the expansionist North - rather than the violently expansionist slavers of the South willingly committing treason in in order to expand slaveholding lands throughout the Americas, something they had attempted previously in Nicaragua, Cuba, and Kansas.
Are there exceptions to all of the above three? Of course. But by and large, nothing would be lost if these monuments were removed and melted down, to be replaced with more fitting figures of veneration from the South if possible.
