Start cutting the cord anyway. Start downloading shows she watches, find them on netflix, etc. Get her used to what it would be like without TV, then see if she would go without. Is it worth $100/month just to watch 1-2 shows you can't find online?
My wife was resistant at first too. And I think it has less to do with availability of shows and more to do with just sitting in front of the TV and finding something to watch. My wife said that, paraphrasing somewhat. She liked to just sit in front of the TV and only half pay attention while she reads pinterest or facebook, or crochets. Luckily, that version of my wife is gone. We watch TV because there's something specific we want to watch and that's it.
Lack of free time from the kid will help too. Some days, watching TV feels almost like a waste, I got other shit I'd rather do.