I coached sports for 20 years. During Fall, we always had tournaments, so I missed most games live. But I taped them. I made sure I stayed off the internet and didnt go near a tv while at our games. Then I would go home, turn on th egame (even though it had been over for hours) Id watch the game and it was as if it were live.
Anyone can do the exact same thing using NFL+... so yes, it is an alternative, and a pretty good one. Considering the fact you get RedZone, as well as NFL Network thrown in, plus the ability to watch any local games LIVE, I think it is a pretty good product.
I am not sure if it will give you the Thursday night games that are on Amazon though.