As someone that has moved from software engineering out into management, I certainly understand your points and from the outside they make a lot of sense. However, I disagree.
As many in the thread have said, the majority of software engineering is contemplating a problem and coming up with workable solution. I remember years ago when tasked with replacing a complex CORBA interface with web services, I spent 8 weeks planning, pondering, and scratching on ether-paper, and 4 on coding and unit test. Because I had done all my planning and designing up front, the actual coding went quickly and I ran into almost no issues. I was done well ahead of schedule and as of several years later when I left the firm, there had been no problems. However, I bet that for those first eight weeks, I sure looked like I was doing jack.
The challenge for most non-software engineers is that what SE's do is so different and unique. We can understand what a mechanical engineer does because most of us have opened the hood of our car and looked at the complexities of the engine. We can grasp at what nuclear engineers do because we've seen large cities and huge ships powered by their works, not to mention read about the probes we've sent to other planets powered by them. We can comprehend what Industrial Engineers do because..uhh..well maybe nobody understands that (joking...joking...).
Software Engineering is so foreign to what other individuals do that it is a mystery. It is part logic and process modeling, part math, and often requires a firm understanding of science and physics. Some tasks require an understanding of human psychology. Coding is one of the steps int the software engineering process, not the only one. It is unfortunate that it is also the only step people seem to attribute to the engineer. Software Engineering is much closer to art than production line work sticking slot A into tab B. And like artists, many of software engineerings practitioners tend to be a bit egotistical, anti-social and well..pricks.
Having said that, if the OP's description is accurate, there is definitely something wrong in his new organization and I agree he should begin to look elsewhere. Either his fellows are indeed lazy or management is setting unrealistic expectations.