I think some important things, at least that I've learned from asking and some not so great experiences, is that it's about expectations.
In the idea of unicorn hunting or couples wanting to date on person, expectations are typically the issue. If the couple expects the unicorn to want exactly what they want. If the expectation is that the couple is the 'base' of the relationship and therefore more important. It leaves the unicorn in a very vulnerable situation!
The same thing can be said about hierarchy. DH and I have personally been flamed more than once for using terms that relate to hierarchy. However, we aren't prescriptive about it. We simply understand that every relationship is different. They move at different paces, they have their own ebb and flow. So it's not a matter of telling someone they have to fill a role in the hierarchy or that they are limited to a certain role or roles. It is about where things just naturally fall.
Labels are misleading, they always will be. They are nothing more than a shorthand to the truth. No two poly people go by the same definition any more than two straight men, gay men, bi women and so forth. The labels are just wider definitions to give you a starting point.
Personally, I love the first post. I thought it did a great job of short handing the different umbrellas that relationships with three can fit under. From there, yes, define it better for yourself. I didn't feel that any of the definitions were derogatory. Yes, there are inherent issues with the unicorn hunters, but by laying them out, perhaps people that truly want a triad can make their expectations a bit more realistic and it will help them find not only what they want, but what works for them!
So many couples decide the best way to start into poly is a triad. I get it, I do. It's safer, at least it seems so. After all, it makes no changes to the 'core' relationship. it's still those two. They just added in! That is a problem however, because I can tell you, each relationship you have changes you as a person, changing as a person will of course change how you work in any other relationship! So it's honestly not any 'safer' for the 'core' relationship then one of you dating separately. That, IMHO, is the part that most couples have the hardest time with. Redefining their own relationship in order to have other relationships.
Me: 40 pansexual poly.
DH: My husband of 21 yrs and father of 3 teen girls.
DC: LDR of +9 years/former