I think you are really talking about two different things. Musashi mentions them in the Gorin no Sho as "utsu" and "ataru" or as what could be conjugated as "uchi" and "ate". I got the feeling that uchi (striking/hitting) was used to distract the opponent and that ate (scoring/hitting) was the decisive stroke in the engagement. Musashi was describing his own strategy and not Aikido, but I think the distinction has merit.
In the Daito Ryu, atemi are used to disable the opponent in some fashion with a throw or pin applied afterwards to control or incapacitate them. Keep in mind these men were all armed. Merely punching them was not a decisive victory; seizure or control of weaponry was critical to survival. Whether it was the change in Japanese society by the abolishment of a weapon wielding class that caused the engagement between people seem less deadly, or the emergence of the modern budo as processes for individual growth, the fact remains that emphasis on atemi became watered down.
O-Sensei described aikido as being 99% atemi, then did nothing to pass along that knowledge in any coherent form. Tomiki and Yoshinkai Aikido are perhaps the only systems to codify atemi into recognizable kata. (Notice that Shioda and Tomiki were both pre-WWII students of Ueshiba.) In time and under the watchful eye of Occupational Forces, atemi lost its roots in most aikido.
Keep in mind it was understood that when engaging in hand to hand combat, if one of the combatants could be subdued via atemi (that being a decisive, staggering strike) the whole thing was over. This was not boxing, which believes in pummeling the opponent until they cannot stand up any more (utsu). Atemi is decisive. If the atemi was unsuccessful, you had better have a backup arsenal and voila! techniques of all shapes and sizes are born! They are all "what if" versions born from that one chance-one cut "ataru" Musashi talks about.
So in my opinion, expecting to go into a combative situation without understanding anything about atemi and just trying to pull off a bunch of techniques is going to get you hurt. We are not just talking about clobbering people, but having a decisive outcome from a conflict. If Ellis Amdur could apply some atemi on an opponent whenever he wants, he is either showing off or his ukes are not paying attention. Aiki is born whenever a moment for decisive victory happens. Everything else is just BS.