It's a fine line to walk - there are plenty of sites around that allow "non professionals" to ask geeky questions of professionals but by the time I joined this site, about 4 years ago, a large part of the drive at the time was to attract IT professionals to the site explicitly because there wasn't any other place for professional-to-professional level help.
That's a large part of what attracted me here - not merely knowing that the responses I'd get to any question I had would contain far less naieve and useless speculation but knowing that the standard of questions I'd get to see and maybe respond to would be of a higher level.
In order to attract and keep good professionals, the site needs to provide an environment they want to be in. While SE could indeed redefine the purpose of the site to allow anyone to ask questions of any standard, doing so could (and already has in some cases) cause the very people they need around to answer those questions to leave the site or greatly decrease the time they spend here.
This isn't talking about keeping newly minted professionals out of the site - it's possible to be a professional and be new to your job (A medical doctor on their first day of work is still a medial doctor, a new lawyer is still a lawyer, for example). To me, developers and devops type people are perfectly welcome here if they're asking on-topic questions in a professional manner but regardless of who's asking, "give me teh router configz and tell me if my server is big enuff for my youtube clone!!!111!!one!one" is just as annoying to us as "give me teh codez" is to Stack Overflow -they'll give you short shrift for the latter every bit as harshly and quickly as we dispense close-hammer justice for the former.
To me, it's not about keeping anyone out at all, but rather about setting a standard for what type of questions we expect to see here, both in terms of what's on topic and how much effort people should be making to produce a clear, well written question.
I especially wouldn't take Jeff's comment too literally - he was asking for "BOFHs" and yet when he was part of SE, he was one of the first people to (rightfully) pop up and tell us to behave if we started behaving too much like actual BOFHs.