These streams are closer to pornography than most people realize. There's a reason that these streams get so much attention: 14 year old young men love watching video games, so they go to sites where they can watch video games. If you start serving softcore pornography on the same website, well gee wiz, who could have guessed that it would be pretty lucrative?
You don't have to be a prude to have a problem with this. It's not a matter of stigmatizing sex work or being anti-women, it's about profiting by serving porn-lite on the same site where children are likely to be.
I don't personally care, but I'm floored that a company like Twitch/Amazon, with hundreds of people in HR and PR, would not play it safe and just ban it.