Well - those two vids above are all well and good but it's nothing to do with Aikido. How are you going to learn aiki if you train like that? Aikido is The Way of Aiki as far as I'm concerened. Atemi in Aikido (or Jujutsu for that matter), if that is what you want to do, simply have to be applied within the flow of the technique.
Your post raises a very common question and suggests a topic that I dont see discussed often.
If aikido is the way of aiki, we might do well to know what aiki means. We can see from aikiweb that the term is still largely undefined, and is up for huge debate at the moment. For that matter, I'm not sure we're all that clear on what do means, but at least there is enough of a common consensus or the term is unimportant enough to us that we dont go rounds and rounds and rounds about it. So, what does aiki mean?
Something I have noticed in a couple arts and that your post reminded me of is that folks do not train well around strikes and flow. Watch a bitchin Bruce Lee nunchaku kata. Holy crap, there are a lot of potential strikes there and a buttload of flow. However, take those chucks, start that kata about 3 feet from a heavy bag, flow really well for a few seconds, and then step into range. The moment the chuck hits the bag all that lovely movement (laminar flow, if you will) is gone and turbulence is introduced. Same with punching a real person. Successful atemi severely changes flow. Those of us training martially could do well to experience that.
I think the first video in that post was pretty realistic and pretty good aikido. The attacks were a bit slow and a little empty, but it is training/testing. What I liked was that the punches were taken seriously and dealt with through covering or small evasions. It was clear to me that the white gi guy respected the effect (the break in flow) blue gi's punches would have. And yes, sloppy-assed haymakers are the order of the day in what I've seen of real attacks and fights. That kind of training doesn't look good to some aikidoka eyes, but it looks real and effective to me. Block and evade until you get the attack that fits the criteria for the techniques you have installed and available at the moment. Hmm, that sentence is related to my current (admittedly limited and external) idea of aiki.
I did not much like the second video because it seemed to combine the best of complaints against aikido from both sides of the aisle. The attacks were real enough (but really empty), but not respected. Instead, they were waded through and much ignored to get to grappling range, Better be really well conditioned to do that reliably. That aikidoka is in for the rude awakening of a real kick to the side of the knee or pop in the liver. Nage does not look comfortable with the change in flow that uke's resistance brings, and kind of hops in and out of range and technique without much regard to flow. He seems to force technique in several places. Maybe training on tatami will smooth out the sweeps from the trapped kicks.