Question

The Rabbi wrote in his latest article regarding polyamory that there is no issue of a married woman, since he betrothed her not on condition that she be exclusively his, and therefore this is not considered valid kiddushin.
So first, assuming that is what the Rabbi meant, allow me to disagree already on the factual level. The truth is that in a large portion of the cases they marry in the regular way (perhaps they were even observant), and only after a few years decided to diversify their sex life. On the halakhic level, why exactly is this a necessary condition for kiddushin? Maybe there is reasoning to say that kiddushin, by definition, is meant to prohibit her to the whole world, but as I understand it that is only rabbinic and not the Torah’s intent.