Personally, I've known enough people who are monogamous in one context and polyamorous in another context (some but not all of whom describe themselves as "becoming polyamorous" and "no longer being polyamorous", as though the context were irrelevant) that I've become somewhat skeptical of the "modifying to become" formulation in this context.

E.g., I've been in a monogamous romantic relationship for ~20 years, and have no particular desire to become romantically involved with anyone else, so I generally describe myself as monogamous. But I can imagine situations in which I would become romantically involved with a second partner. I would change my self-description in that case, but I wouldn't consider it a particularly significant self-modification.

The map is not the territory, etc.

Regardless, yes, many people can be happy in certain kinds of polyamorous relationships (for example, closed polyads as you describe), and not others. This should not be surprising.