I don't see anything wrong with getting your child into a car that has nannies up the wazoo. When it comes to safety, you want to have the tech that can react faster than the driver can, especially when the driver is inexperienced or easily distracted (most teens). Even if you're the most attentive driver, there are certain situations that you have no control over, where the safety tech really shines (i.e. Pedestrian Detection - a child running out into the street from behind a parked car).
With that said, I agree with Uno and Nelson that they should learn how to drive without relying on the safety tech. Typically, if an inexperienced driver gets used to the BSM going off instead of shoulder checking, the BSM becomes a safety net and the basic technique of shoulder-checking isn't reinforced. If they know the car will brake for them if it detects a potential collision, they'll be more likely to give in to distractions like cellphones or unruly passengers because of that safety net.
My suggestion would be to get your child a car with the nannies, but don't tell her about them. Don't teach her how the BSM works, don't teach her about the auto-braking or even the traction control. This way, she learns how to drive without relying on the tech, and you have the added peace of mind of knowing that the tech is there and working, just in case.