Why Doesn't Software Engineering Get Respect?

I have a serious question for which I'd love serious replies.

Why is software engineering treated with so little respect? I cannot think of another job where experience seems to count for so little. Would you rather have a doctor fresh out of medical school or a doctor who's been practicing for 10 years performing your operation? Would you rather a journeyman plumber work on plumbing your new construction or a master plumber? Yet as far as the creation of software, experience seems to count for almost nothing.

Now, as I said, this is a serious question. I realize there are some mitigating factors in play:

1. Software development technology changes rapidly. If developers don't keep up with technology they become worse than useless; they're actually a drag on accomplishing the goals of the project.
2. It's extremely hard to measure productivity of a software engineer. So there's no metric to point at to show that a senior software engineer is more productive than a junior. We end up relying on experienced business people who've interacted with IT in the past to recognize that it's worth their while to find experienced developers.
3. The career path of the software engineer (with few exceptions) seems to always lead to management. I have never understood the logic of taking someone who's very good at programming a computer (which doesn't seem to require a great deal of emotional intelligence) and deciding their next, best career step is supervision (which does seem to require a lot of emotional intelligence). Hence people don't have a lot of incentive to stay with software engineering.

I'd just like to hear other folks take on this question. How do we get more respect for the job of software engineer? Or am I totally off-base in thinking that our job is treated with very little respect for professional experience?

Please comment on this; I would love to hear the thoughts of software professionals and other business people outside of IT as well.