On the topic of toppling statutes of controversial characters, it might be worthwhile to explore what exactly the point of statues even is. The token argument against destroying statutes, no matter how awful the person depicted is, is that it is a form of erasing history.
I see quite a significant difference between putting a statue on a pedestal in public versus displaying it in a museum. The public pedestal is a form of veneration, and it doesn't strike me that all persons venerated in the past are equally worthy of veneration today. Someone may say that the statue is a concrete record of history, which it absolutely is, but it's not only that and not everyone sees it as only that. For Confederate memorials in particular, the vast majority were sprung up in two waves, first in the 1900s then second in the 1950s. Both periods happen to coincide with significant racial tension (Jim Crow and desegregation respectively).
Considering also how the monuments were mass-produced and cheaply made makes the timing further suspicious. To me, the evidence seems clear that the motivation behind this sudden desire to memorialize the Lost Cause looks a lot more like trolling rather than an earnest attempt to document history. I'm imagining what the reaction would be to commissioning heroic looking sculptures of a prototypical Wehrmacht trooper with a caption honoring all those who served, and installing that outside the Holocaust Memorial in Berlin. Sure, you can say that you're just trying to document history wouldn't it strike you as a bit weird? I would not assume that person is operating from a position of good faith.
The monuments still deserve protection as snapshots of history. But putting them in prominent public spaces is interpreted by pretty much everyone as a manifestation of veneration. It's along the same scale as naming streets, parks, and buildings after people. It's a way for society to say "You did a great thing! Have an airport." I gather that almost no one views public pedestals as neutral spaces of a historical snapshot.
One potential solution to the current wave of iconoclasm is to just privatize everything:
We no longer agree—if we ever did—on which qualities should be celebrated and what failings should be overlooked. We're increasingly vocal about such disagreements, to the point that people are willing to tear down statues that offend them, and any future images are bound to cause more offense.
A statue on private property, erected with funds only from supporters, dragoons no unwilling parties into the message it expresses. Nobody need feel that they're being forced to share in the celebration of people or ideals they oppose. A private construction can be left up as long as it pleases the owners or pulled down at their whim.
Seems reasonable to me. The particularly salient point is that first quoted sentence, about how it's impossible for us to agree on which qualities to celebrate. This turns every memorial into a sort of referendum about that individual, which inevitably is a losing proposition. Governments can stick to providing the basic traditional services and let the private sector decide what's worth venerating. With the government out of the business, it doesn't strike me that funds for commemoration would be scarce. This is especially true if it is no longer possible for politicians to dedicate funds without at least one segment of the population losing their shit over the choice.