Requiring consent would limit the lifestyle choices of the husband and his new bride--the old one would have no power to stop him, and would find taking it to court rather difficult since the definitions are always free (unstable). And, how dare you try to exclude a needy new wife (and baby!) from health benefits and housing!
Given the way polygamy has worked in the past, I'd say many first wives would find themselves hard-pressed by circumstances not only to accept the new defintions of marriage, but to put a good face on it--
The only way I see a woman maintaining a strong hand would be to insist that all property be in her name, and also insisting on a prenup that, on the event of a new wife, her "dowry" remains hers. These are typical marital contracts in a few Muslim countries.
Personally, I have great faith in the ability of the American Woman to decide that she will not put up with this kind of cr@p. And as for those women too stupid or weak-willed to refuse to be doormats for men: well, they're already living in the projects or the trailer park with three kids by three different men, none of whom they've ever been married to, so I fail to see how using the state to enforce a theologically based definition of marriage will help them.