If you can time the attack to do something than that assumes you have a great deal of control of the situation. Of course you would do something like tenkan or irimi.
The problem with reality is that you may not have that amount of control. Chances are you don't. so you are managing a very difficult situation where you are trying to not lose ground, manage the fight and turn it around in your favor.
In a empty hand or even knife range it becomes all about the clinch...which fundamentally is exactly the same principles you employ in irimi tenkan, iriminage and a multitude of other attacks that we tradtionally practice in aikido.
The problem in a real fight is not that what you learn in aikido is wrong or will not work...it just that you will typically practice at a perfect range that is maintained cooperatively by both participants. In reality that range and distance is closed down very closely because you each of you wants to impose your will on the other and therefore you get close and very intimate very quickly!
My advice is to learn the clinch and to practice it. After you get the hang of the basics, you I believe you will begin to see things you have learned in aikido popping out of the clinch...albeit maybe it does not look or feel quite the same but principles and basics are there.
The clinch is the best place to start if you want to transition from traditional attacks to more realistic attacks.
How essential is atemi in a street fight? very essential. However it is secondary to control. You can't effectively do much if you are not dominating or controlling the fight. Atemi is useful to disrupt your opponents game plan if you are losing or behind in the OODA loop. It can create distance, space and opportunities for you to regain ground/control. Once you are in control it is useful to maintain control or to submit your opponent to a condition where he is no longer a threat. Watch any UFC for the stages of a fight and you can find many good examples of how atemi is used in conjunction with both the losing side of the fight and the dominate side of the fight.
I like that you brought up the clinch. In doing Muay Thai, some BJJ, and other grappling styles, I've found the clinch to be quite useful but once in it, how do you use Aikido? Personally, I'll throw knees all day but that's not exactly Aikido. Maybe a knee to the groin, then a throw followed afterwards but more than likely, unless you strike FIRST in the clinch, it's going to be a wrestling match. Especially with someone who has no martial training. So what are some specific techniques you could employ in the clinch, in your opinion?
I do believe, though, that Aikido is somewhat of a clinching art. Most just don't realize that when you do close that distance into the clinch, it will become a grappling match. Not a one-sided, kokyunage throw.