Nah…If one goes out, they just jack up your bill. (Especially if you have Comcast!) And,if you're lucky, they might send out someone to take a look …in a week or 2.
No, they’re not totally independent of each other. If the TV goes out there’s no internet, but the internet can go down the TV still works – sometimes.
Yes, I bundle… TV and internet - $200/mo. (outrageous!) I’m going to have to cancel the TV very soon as they keep jacking up the price and cutting down on the amount of channels.