This seems like Chesterton is making it up completely. Most progressives base the impulse on the hope that things could be better; dealing with the decay of conservatism is not a hypothesis that even enters in their minds. The 'truth of conservatism' (at least, the straw-conservatism defined by Chesterton here) is taken for granted by most people: if things keep on going like this, they'll keep on being like this.

No one has ever become a feminist by saying 'my god! if we leave things alone, the patriarchy will keep becoming even more oppressive and brutal with each year! We need to fight this slide of the status quo, and incidentally, it would be nice if we could not just repair the rot but also yank the status quo towards feminism and get women the vote and stuff like that'.

No, it tends to be more like 'the status quo is awful! Let's try to move it towards getting women the vote and stuff like that'.