Because even if you try to make it clear that it's a consensual act (sex, relationship, whatever) between any group of people of age, the people against such a

Because even if you try to make it clear that it's a consensual act (sex, relationship, whatever) between any group of people of age, the people against such a movement will claim that you are a pedophile, that it's against (insert some religion)'s beliefs for a union to be between more than two people, etc. The people who don't know better and don't think of polyamory as mainstream will find that emotionally appealing. In the end you have a mess (see: same sex marriages today) where you think people should know better and realize this isn't about what's "right or wrong" to any individual on any level, but a matter of discrimination when it comes to benefits that are not being given to one group but to another. But they don't always know better. In the US, we're barely scraping by trying to get the same benefits to gay couples, let alone any mix of more than two people. A movement to do what you suggest...I can't imagine what kind of uproar there will be and how many people will be conflating polyamory with polygamy and being very against it as a result. At the minimum.