Good points Maggie and Ryan.
I always figured a few bruised ribs or a busted lip helps teach you how not to get hit. I mean, no one pads a real knife. You might get killed some day if you train your mind to not respect a blade.
This is how we tend to train (in my Tomiki dojo). Unless we are doing specific competition training all knife work is done using a wooden replica of a real knife (painted silver and shaped accordingly). I have found that this helps the student to keep the respect for the tanto as a potential weapon for non-sport situations. It also encourages the use of Aiki principles in a way that will maximize safety if one is faced with a knife or similar situation.
Of course there are a lot of things that are tactically wrong (from a self defence or combat perspective) when we look at sport-style tanto randori but the key I guess is to remember that it is just that - sport. The primary job of the knife is to enforce correct ma ai and prevent the encounter from becoming a Judo match. The tanto forces both participants to maintain a certain ma ai that increases the possibility of executing Aikido waza under those conditions (and simultaneously minimizing the potential for close range throws, reaps and ne waza).
Regarding the "Aikikai approach" to randori, it depends on the instructor as in most cases. I have never experienced that form of randori in my Aikikai practice (or Yoshinkan for that matter), but I also know that depending on the instructor, the possibility of that kind of training is definitely there and is often done by Yudansha with a similar desire to train that way.
Sometimes the Aikikai approach may even be more comprehensive as it allows one to deal with more attacks than just a tsuki. This is critical for developing the proper reflex responses for non-sport applications of Aikido waza. I have adopted this training method as it is also part of Shodokan Aikido but not often used by those who focus primarily on shiai.
Just my 5 cents.