The Jedi, like Blockbusters, thought they were going to be around forever, but now their premises are occupied by people indifferent to whatever it is they actually did.
I don't actually know what happened in any version of canon, but I'd imagine Palpatine would want the building demolished for sure to erase a visible Jedi legacy. Maybe put a giant Clone Wars memorial up celebrating "true" heroes of the war like various Republic officers killed and imply they would have supported the turn into the Empire as so many of the surviving ones did.