Are you suggesting that if a family has any kid older than 6 (while also having one under 6), they're not supposed to use family boarding? Because that really doesn't seem to be the words on SW's website and it seems to be what you're saying. Nor do I quite get the two adult thing (are you suggesting that single parents wouldn't be able to use family boarding if their kids are under 6 since they reference two adults? Logically, does it quite add up to you that if family boarding is meant for families with kids under 6 that making it more complicated for those families would be beneficial to any part of the boarding process?). If anything, a single parent with a kid under 6 (even if I have one over 6) probably can use the time since kids under 6 can be hard to direct and get into the plane (and fwiw, many of the families returning and using family boarding - I paid less attention departing - seemed to only have kids over 6 instead of one in each group like I had). At no point did anyone ask about the age of kids when scanning passes (though I presume they might've all come up on the screen - maybe not) - but I can't wrap my head around what seems to be your suggestion that because I was one adult and/or had one kid over 6, I wouldn't have met the requirements for (or benefitted from) family boarding.
As you mentioned what you diagnose as my mistake, you seem to be correct - though I had specifically asked about it since I was using the CP earned through the CC as well as points. I had understood that since reservations for a minor traveling with me would be connected to my boarding pass, this would make sense (and I think I literally wrote that out far before the trip in this long thread) and somewhere along the way I got it wrong. I now know that it's a poor use of the SW card, CP, points, etc and won't make the same mistake (and hopefully others can avoid it). I mean you said something like "everyone would do this" but I spent more funds purchasing the Business Select ticket than I would've had I simply purchased EBCI for the three of us (which I couldn't figure out how to do with the CP) and this seemed like the simplest/least expensive way to do what I needed (which was have time to board with my two kids as a single parent, managing one of them - the 5 year old - for their first flight ever). Obviously, yes, I could have bought all three of us Business Select tickets, even forgoing the Companion Pass and points I had earned over the previous 6-12 months. Maybe your implication is that if you have kids, you should spend as much money as possible?
A simple acknowledgement from a gate agent, "You seem to have your hands full" would have been representative of the typical good customer service and friendliness that Southwest is known for; that didn't happen. Not unlike Guest Relations at Disney Parks (or really any customer facing job anywhere), simply acknowledging a customer's story can go a long way to helping them feel like they had a positive interaction. In my current job, I'm regularly discouraged from making a problem that occurred - even if it's absolutely clear the customer made a mistake - about the customer's fault (and instead am told to say things like, "I'm sorry this didn't go as planned - how can I help in the moment?"). But, it's a stressful job (the gate agent), it's 5:30am, and I recognize she may not have had a ton of time to think on her feet to say anything like, "Yeah, this really does stink for you because you had an expectation and it's not being met, regardless of how we got there." At that point, it's not about "rectifying" a situation (this is where I often think people on the boards go wrong with expecting Disney to offer "pixie dust") so much as a positive interaction with another human (or, at the absolute least, not a negative interaction which is what I had). And if that's asking too much, then I do think it makes sense that I don't go out of my way to give them business (which I've been doing since just before covid). It's not a slight against the person or company - just an honest to god consideration of what they say at the end of each flight ("we realize you have a choice as to who you fly").