Re: atemi at end of technique
The OP was asking a question about a particular thing - a finishing strike, performed after a technique; more accurately, performed at the end of a kata.
Mainline Daito ryu calls this a todome and I do not believe it is functional. It is a tegatana strike that represents drawing a short sword and finishing the attacker. I don't think a tegatana strike is particularly good for finishing a downed attacker, but anyway, the emphasis is clearly on zanshin and kiai as opposed to how you should be striking them to hurt or finish them off with your hand.
I do find the question of why this was dropped from mainstream Aikido to be interesting and I wish we could have had that discussion. I can tell you that my Aikido tradition eschews this symbol because we would rather demonstrate the absense of it - protecting your attacker, not killing them, etc.
Classical jujutsu systems often have quite functional finishing strikes in their kata. You might see uke thrown, and nage, without really waiting for them to hit the ground, will launch a backfist to their temple or their jaw. There are also finishing techniques that are not strikes, for example chokes.
I have seen Aikido instructors point these types of technique out many times, but in my tradition we don't include them as part of the general technique (as, for example, you would perform for a test). In my opinion it is best to study them as part of a pre-arranged kata because if you throw them in at random eventually someone's head or throat is going to be in the wrong place at the wrong time.