I don't think anyone will attack you for asking that question. In fact, I want to genuinely hear rational, valid arguments that support it - I'm always open to changing my mind, when presented with different facts and perspectives.
But, let me counter that question by asking this one: what qualifies a coach to be a good judge of officials? Most 3rd year officials have a more through understanding of the rules than most coaches (IMO), and coaches have next zero knowledge of mechanics. They have no objective lens to look through, nor any even defined criteria as to what makes a crew championship worthy. In a quarterfinal game this year, two DPIs were marked off incorrectly as spot fouls (I think one was marked off as 26 yard DPI, in a fairly close game). Didn't see the coach on the short end of the stick screaming at the R, on either occasion, as far as I know - most coaches would be besides themselves with a mistake like that going against them, in those circumstances.
I'll acknowledge you have a valid point: they are the only ones involved in the game process who do the job full time. That is an an element that I have not considered.
That said, I just don't see how it benefits, as opposed to harms, officials, and officiating in general, to have coaches pick crews. I can't think of any other football level, or other sport in general, at any level, that thinks allowing coaches to pick the judge and jury for their games, is a good thing, for the game.
The other, more ugly reason, is that while we all want to say we are a noble and honorable sort of folk, the reality is that we are not all that way, and solicitation absolutely is a thing. I have personally heard officials brag about their crew reaching out to a coach they were friendly with to make sure they got a certain game on a certain week, during their draft. And solicitation is enabled 100% by allowing coaches to pick.
Lastly - it does have to do with 'spreading the wealth' around. Every single chapter has crews that are capable, and deserving, or working quarter and above, including championships. The El Paso Chapter this year, had at least 4-5 playoff games in their backyard - and they received zero playoff assignments. Not a single one, at any round. In a chapter with over 200 members. A handful of other chapters got completely blanked as well. Why would someone want to work hard, hone their craft, only to be systematically excluded from the sport’s biggest stage? (And don’t do yourself a disservice by saying officials do it for the kids – if that was the case, we’d all work for free (as would coaches) and how many coaches would stick around, year after year, knowing that regardless of the time and effort and sacrifices made, they would be excluded from the playoffs, or championship games?)
I simply don't understand why some don't want to have a system to give everyone an equal shot to work championship games. I'm in a small chapter (7th smallest, which edged out the three directly below by a total of 4 people), and I'm resigned to the fact that under the current system, the odds of me ever, in my career, working a championship game are virtually nonexistent. And yes, I would likely benefit from a change, so yes, I am biased. But even if I don't ever call a championship game, I hope that the advocacy I bring helps other officials in small chapters have the same opportunities and chances as the large metro chapters.
//off soapbox//