I've never understood the phenomenon of taking down statutes. Seems to tie in with the whole purity spiral thing... Whereby people are expected to be ultra pure or ultra evil and the same dichotomy is thrown onto historical figures - they were either a shining light of pure goodness or an incarnation of the devil. And we must banish all these idols to erected to demons... Or something along those lines.
I think it ties into free speech because this kind of historical awareness helps us remain open-minded, and also is a warning against hubris. The monuments of the past are a reminder that ideas and people that are powerful now are not more likely to be correct and good. Our statues and our gods are no more likely to be pure than those of the people of the past.
I think part of the reason it caught on in the US is that their history is shorter. No one in their right mind would expect to look back at someone like Albert the Great and see that his opinions on political or social issues were in line with current thought. And in general in the UK and Europe you see all kinds of statues and monuments and plaques commemorating diametrically opposed persons and principles, sometimes right next to each other. Somehow Americans expect their founding fathers and the principles of the nation to have been equally good and right all along.
The American approach reminds me of nothing so much as seeing a spoof on tv as a child of Russians tearing down and replacing statues as the political winds change. Talk about mirror images. Neither societies being entirely comfortable with free thought.