Mostly agree with you .
Till up and loosen the soil( even in raised bed) , then put plastic over it to sterilize the soil.
The reason why I suggest some tillage is to get the heat down deeper into the soil, until the soil temp registers either 160 degrees, or at least 140+ degrees for 5 days.
Good point and I would do that as well. Also, if it's a raised bed bring the black plastic all the way around to the ground level.