Think about it from a business directors perspective. Many engineering jobs and job functions can be outsourced to a much cheaper area. Engineers are critical to a firms bottom line but many positions can be done for a lower cost. A nurses work on the other hand cannot be outsourced. Perfect market competition is a myth and the dynamics of a newly formed global economy has made things worse.
Why don't practicing physicists or chemists make good money? Their degrees represent a similar level of difficulty and require a similar level of intelligence as an engineering degree. It's because there is not a large domestic need for the work. The work of these two professionals can often be sent overseas.
But we don't do things just for the money. If money was the only thing to consider you could go into the right sales field and make more money than an RN with just a business degree.
I got a BS in chemical engineering and an associates degree in electrical and computer engineering. My BS was from a top UC. I now work in healthcare as a clinical support specialist instructing surgeons on the proper use of surgical navigation equipment for doing spine and cranial surgery. I am there in the OR helping to orchestrate the use of the technology. I am on call often. I make significantly less than an entry level RN in my area. But I like the work and I know what I do helps people and at the end of the year they want me to take on additional business development duties. If I agree, my income will be significantly above an RN. I graduated under a year ago.
I get your frustration. It can be difficult to find well paying and rewarding engineering work in this market. Especially entry level work. It's also annoying that high school students are told engineers are in high demand and command high pay when they really command average pay and are not in high demand.
I use to tutor a lot of nurses (and premeds) in chemistry, math and physics courses and I watched as many of them partied in college while engineers hit the books on their Friday and Saturday evenings. The nursing profession is akin to most trade work. Look at people who go into a pipe fitting union or masonry or HVAC. They make good money, the work is important but they didn't have to work as hard or risk as much (in terms of debt and duration), and the average student is not as intelligent as an engineering/physics student.
Intelligence is not enough to make you more valuable. Nor is being hard working. It makes you unique in the scheme of things, but until you figure out how you can apply those traits to gain the right blend of skills it's not that valuable of an asset in a professional setting right now.