Of course, while I've never had a professional software engineering gig either, I do have previous experience with development and other paid jobs in supporting roles like systems administration. I sometimes think that it's simply a consequence of the barrier to entry being so relatively low. Do you have a computer (or even access to one that you can install software on) and access to the net? Congratulations. You have everything you need to start learning about concepts and tools that are immediately applicable and relevant to the field. And they're Free as in Freedom to boot! So long as you have the time, you have all you need to get to a point where your horns aren't entirely green and the spaces behind your ears aren't entirely soaked. With guidance from more senior devs, you'll get to their level too in no time at all.
But it seems no matter what I do, it's always the software guys that are interested in talking. They're so interested, it seems, that I don't even have to go to them. They'll come to me. Which is honestly shocking, given that I still consider myself a very sophomoric developer. By contrast, even getting the hardware folks to show up seems impossible. There was a recent STEM job fair at my university (Texas State) that really ought to have been billed as the Computer Science job fair. Sure, Freescale and National Instruments were there, but there weren't any members from their hardware or verification teams. It was all software and IT. Samsung was there, but I honestly don't know why. I didn't need a hard copy of the job description that was printed from the online job site. Apple was there, but they were only looking for at-home tech support. Intel wasn't even there. AMD wasn't even there. NVIDIA wasn't even there. Cisco wasn't even there. And those are all companies with established offices in the Austin area.
My heart may be in hardware, but I still love software. And guess who's hiring. And guess who's got student loans to pay off :D
tl;dr: Yes, I'd say the problem does exist. And perhaps the reason why web apps are so dominant and "infrastructural elements" so maligned is that the barriers to entry are so different in each field, and the corresponding willingness to train in each field seemingly reversed.