I think it would depend where we draw the line on Earth's history and the time distribution of these impacts. During the early days of the Solar System huge impacts would have been part of "the old normal", but there's a limit to how many massive rocks there are to go around.

On a side note, I didn't find that video particularly impressive–of course the impact of an asteroid whose diameter is larger than the width of bloody Japan would be apocalyptic! I also found it a bit gratuitous when they showed recognisable landmarks looking a bit damaged when the whole world is lava, and pointless that they talked about the effects "a month" later. What is even "a month", if not even the extremophile archaea survive?