Also tackles above the waist are forbidden. In American Football you can pretty much just throw your entire body anywhere, with unsurprising results.

It is tackles above the shoulder (not waist) that are forbidden (along with striking an opponent with a stiff-arm whilst tackling, tripping, picking up and dropping a player etc.).

Law 10.4 specifies what is considered 'dangerous play': http://laws.worldrugby.org/?law=10.4

this video disagrees with your claim about rugby: https://www.youtube.com/watch?v=rZ1Mt0LdCfY

Fouls happen. I don't mean to diminish that, but when the base of the game is to disallow bad tackles then there will be far fewer incidents of bad tackling.

You can't tackle someone around the neck in rugby or too high, it's a foul called a "high tackle"

It's also that American football has a lot of downtime between the relatively short plays, whereas Rugby has a more constant style of play. An entire NFL game consists of roughly 11-12 minutes of actual gameplay -- the most recent numbers for rugby I could find put it at ~35 minutes. So, players are less fatigued and can hit harder and faster.

Also many more substitutions, which plays into exactly the idea you mentioned.