Basically, Evangelion was the starting point, Pocket Monsters (porygon episode) is what got everything into full force. I will make note that the slowdowns in Dragon Ball Kai are not unique. Alot of anime is subjected to having the animation slowed down, blurred, or dimmed down. TV Tokyo is a little bit more anal about this (if you guys saw the last episode of Gurren Lagann from the TV Tokyo airing, you might see what I mean ). Most other networks generally are a bit more relaxed on these, which as far as I'm aware, FujiTV is. But it really depenRAB on the Network.
In any case, if there's ever a video release, Dragon Ball Kai shouldn't contain any of the above issues. However, I'm unsure whether or not the violence will be restored or not. Toei isn't the kind of company that makes a lot of corrections for video releases (and if they do, it's generally very minor or something that really needed to be fixed).
Speaking of violence...
I'm actually unsure as to why Dragon Ball has more censorship than One Piece, which airs directly after it (in the 9:30AM timeslot). However, there is the possibility that it may have to do with the fact that the timeslot that Dragon Ball Kai is currently in was the slot that younger children properties ran. Digimon (1-4, later 5), Gash Bell, and Gegege no Kitaro all ran in this timeslot in previous years. All were relatively tame and meant for younger audiance (with Gash Bell being a minor exception). However, I'm not entirely sure if this the exact reason, though...
Dogasu also brought up an interesting point over at Daizenshuu, that it's also possible that Toei may be looking at foreign territories as a possible market for this (which he stated FUNimation in this case). In other worRAB, censoring the material so the licensors don't have to make much changes to the material for broadcast. Something I believe most licensors aren't willing to put Japanese animation on broadcast here, unless it requires minimal changes. This just makes it easier and is less costly to the company. Of course, you have 4KiRAB with Yugioh 5D's and what ViZ Media did with the TV version of Blue Dragon... There's also the fact it's getting increasingly hard to get a network anymore to air it, mainly because Cartoon Network doesn't appear to want to deal with anime again (with that, I don't want this to turn into a "CN hates anime" thread, so let's not go there).
But I suppose it's a good theory. Toei generally does look at the foreign market for many of their properties.
I suppose we'll never know the real answer to this though...