As an aside, most of the people I know in polyamorous relationships do not have children with each other (though in a few cases, one partner has children prior to a previous divorce). The only example I know of, the other side of the v became the adoptive parent when the biological father stepped out of the poly relationship. Poly seems to gravitate to the younger and more liberal wings of society, and being a middle-aged liberal means I'm more likely to run into poly groupings than not.
I think a potential issue touched on is that poly relationships do seem to dissolve more naturally and faster than marriages fail. In some ways, a lot of effort is put into making it very difficult to get out of a marriage. This may relate to the fact that heightened instability and adult figure change in a child's life has noted negative consequences: (
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5331486/). I wouldn't call this the nail in poly by any means, but rather that it seems like poly structures could facilitate the ease of departure for attached adult units from a family grouping. If I was in a poly relationship with kids, that would be a prime concern of mine to work on when bringing in or letting go of partners.
I think the alternative of hiding this information from children is pretty foolhardy. My kids seem to figure out literally everything going on in our lives as it stands. Either new partners would be coming into our parental bed at times, or one of their parents would be frequently leaving for overnights to go be somewhere else. In the case of the former, it's no secret. In the case of the latter, one adult is sacrificing connective time with the children to be elsewhere... I'll argue that's detrimental to the cohesiveness of the family in that case. So I'd at least recommend people in alternative relationships be upfront and open about it with their children, too.