Taking your initial post somewhat out of order, my responses follow.
This is probably massively TL;DR, but you really brought it upon yourself :-)
As a systems admin I often come on here looking for the answer to an obscure question.
Excellent. That's what we're here for.
We need good quality questions but who cares if there are noobish questions too, that is what search is for.
We need good questions. It does not matter who is asking them so long as they fit the scope and intent of the site.
Certain "noobish" questions are simply below the threshold: "How do I Unix?" is why we have Unix and Linux, "What's the default password for a Linksys Frobnitz 5000?" is why we have Google.
A Professional knows and understands these things (either inherently, or after the first time it's explained to them), and does not use ServerFault as their own personal lazyweb. Professionals do real research, make an effort to solve the problem, and post a good, answerable question of reasonable scope (i.e. something more than "Apache is broken. Halp?") for us to work with.
The best way to get an answer to that is to have the widest audience/knowledgebase possible, not the most specialised one.
I reject your premise, because I think you mean to say
the best way to get a GOOD answer.
Having the widest audience/knowledge base possible certainly guarantees an answer, but wrong or frankly stupid answers don't help anyone.
For example, "Pay the ransomware company" will stop the annoying popups your users are getting because they installed the PwnMySystem toolbar, but it doesn't solve the problem that their machines are compromised.
I don't care who asked or answered my question, be it another sysadmin, a developer or shock horror a home user/amateur.
So long as the questions and answers are of good quality I really don't care where they come from either. Similarly if a developer or home user asks a good question that is relevant in the context of professional system and network administration I have no problem with that.
Close by Regex because the question says "home network" or "I'm a Developer" somewhere is a poor standard -- if removing those words leaves you with an on-topic question the question is on-topic.
No one is obliged to answer anything they don't want to.
Conversely, Posting a question on a Stack Exchange site does not magically entitle someone to an answer. Some questions are off topic, out of scope, or simply crap.
That's why "On Hold" exists - either the question will be improved, or it will be abandoned, but at least it's out of everyone's face and not getting hundreds of downvotes while the OP works on it.
If the OP elects not to work on a question to make it answerable or on-topic that's their choice -- I can't force them to write good questions. I won't try to force the community to answer bad ones.
It doesn't matter if there is collateral help for others in the process of working in the interests of the sysadmin. The current focus on trying to expel these other people at all costs harms the usefulness of the site to those like me, the target professional sysadmin!
Is the current focus helping make the place more useful or are people trying too hard to be orderly?
The focus is on quality.
Do you seriously think this is a high quality system administration question?
Do you think Server Fault is harmed by questions of that type being closed?
Addn: the idea of this is for people to stop and question their assumptions and open a discussion. Not for the vocal minority to shoot it down without considering what is best for the site or the wants of majority of users.
The "vocal minority" you speak of represent a substantial number of "answerers" on the site.
The group you see represented here so far ranges from 115 to well over 2000 answers - mostly good to excellent quality.
They are also among the most active voters on the site, and many of them have asked excellent questions as well.
Frankly when those people tell me we have a quality problem I sit up and take notice - most of them are smarter than I am and tend to know what they're talking about, which makes them exactly the kind of people I want to attract to the site.
Gamification doesn't work forever on sysadmins - we see how the system works, and we play a different game (big game hunting for intellectual stimulation).
The E-Peen of "reputation score" isn't why we're here. We're here because we want to learn and see new/interesting things that may not come up in our environments.
If the only questions the site is attracting are ones that can be answered by literally the first result in a Google search for the question title that is not conducive to intellectual stimulation, and the site will wither and die.