"a Gerber file. Is this the best the industry and professionals who collectively all but created the Digital Revolution can put forth?"
Speaking as one who's pretty close to the venerable Gerber file on a day to day basis, I could rant on the evils of the Gerber format. And, I know a few other people who could significantly out-rant me on that subject.
There is some hope though. ODB++ (a somewhat-standard CAD data format) is gaining popularity and IPC-2581 (a supposedly even more standard CAD data format) is on the horizon.
Bills of materials are headache near the scale of the Gerber as well. I think there are more BOM styles than there are engineers creating BOMs.
Your primary point in terms of the accomplishments of the hardware engineering community (Note this) is certainly valid. Electronic systems have certainly progressed rapidly and provided the basis for any number of advances in modern society. I would have backed it up a bit to at least the development of radio and TV myself, which have molded modern society in many ways.
On the other hand, this has not occurred in a vacuum. The software disciplines that you say are "...admittedly less complex" have moved from being a rarefied specialty to becoming a sophisticated and very complex industry to help users do useful things with the electronics you create. In fact, the Web (or, more correctly, the Internet) is generally considered to be the most complex engineering artifact created by mankind to date. From one point of view it is a collection of hardware devices, but it is also a triumph of software engineering. It is also an excellent combination of free enterprise and governmental support.
As to your secondary point about design interchange, it might be worth looking at some software innovations. Much work has been done in terms of defining design patterns, where specific solutions have been classified and analyzed to promote consistency on how they are handled. There are also significant repositories of code that are being created in open source domains such as SourceForge which can be of tremendous help. Recently this is starting to happen with significant hardware designs as well, which is probably a very good sign for the continuance of innovation in electronics.
As I said, there are very good reasons for pride. Be careful, though, that it doesn't become hubris.
A big benefit of using digital circuit designs (rather than a PDF image of a design) is that when new technologies develop - such as narrower traces or components that replace a portion of the circuit - the circuit could be automatically redrawn and compacted from the digital file.
you are correct the engineer is the superstar of the modern world and sadly no one excpet us knows about the impacts we have from advanced medical technologies CT, MRI. To chemical engineers who allow modrn drugs to be mass produced Aerospace (how many people take flying safely for granted), Information Technology these two alone have made the world much smaller place. Then we have the utilities power, gas and water always present when we demand them.
Engineers truly created the world more so than any other profresssion I would argue.