Jobs for many engineering degree holders have near zero growth level,

This isn't quite true. Engineers are still in very high demand, especially in certain areas. Look at the occupational handbook, even the "worst" engineering fields still have an average growth rate. http://www.bls.gov/ooh/architecture-and-engineering/mechanical-engineers.htm#tab-6

Talk to some of your local professionals. Any one of them will talk about how they can't get enough engineers to fulfill their needs, particularly at software companies, where they're having to relocate from big cities and look overseas to get enough. If you're curious, check out the occupational outlook handbook provided by the U.S Bureau of labor statistics for Mechanical engineers

It's hovering at 5%, and it's already a very established industry. Heck look at this 2011 profile for engineers. They saw a growth rate of new degrees of 5.6, very similar to the rate of new jobs for 2015.

In addition, you have to remember that "mechanical engineering degrees" do not just go into the narrow definition of the Labor Bureau. "Mechanical engineers" go into properties, aerospace, design, maintenance, robotic, etc. The list goes on and on, but they are classified separately by each the handbook.

I mean heck, if you look at the profile I linked, the mechanical degrees I linked only had the number at 19,000, and it's by far the largest branch. With 15,000 new jobs(Not including people naturally leaving the field,) for strictly mechanical jobs, how does this indicate a problem at all?