One thing to keep in mind is this is just an observation from a not-so-big anime fan - I really don't watch anime and am basing this mostly on the countless clips I've seen of older and newer anime, so many of you are likely much more educated than I am on this subject.
I've seen clips of older anime in which you'd expect gratuitous violence, like Violence Jack or GenoCyber (which notably is much more graphic than what you'd even find in recent "violent" anime shows). I guess Fist of the North Star could fit in that category too. But even more mainstream stuff like oldskool Macross has people getting crushed and eyeballs exploding. Space Runaway Ideon's finale has (SPOILERS but c'mon it's a 30 year old anime) everyone, even kids, getting blown to pieces. Princess Mononoke has people getting beheaded and dismembered and the like. Evangelion also saw kids getting brutally injured or murdered. Berserk is an obvious one.
By "older" I generally mean anime from the 70's-90's. Everything starting in the 00's, as far as I can tell, started to get much more tame. There's the occasional violence gore galore anime like Elfen Lied, but that was the defining characteristic of that series. You don't really find it so casually as you did 10-20 odd years ago, from what I can see (again, coming from someone who doesn't really watch a lot of anime).
Out of pure curiosity, could someone explain to me what shifted this tone in violence (if anything)?