At one place I worked, they ended a sprint on day n and then turned around and started the next sprint on day n+1. Every two weeks, we started a "new sprint." I grew increasingly cynical about their motives. Some suggest that you're supposed to have some down time in between sprints to look at the code and come up with a plan for the next sprint. A time of reflection. Not at this job.
I absolutely agree with the overall sentiment and I relate very strongly with all the points, except that 2 weeks isn't the norm at all in scrum or agile... It's not standardized as such or made official anywhere so maybe if you made your sprints, say, an arbitrary number > 2,like 5,would things be better then?