To say that Osu should not be used in an Aikido dojo is a little bit of a narrow view. I prefer my students to use it. I have already posted a link that explains the meaning and context of Osu within Aikido, but here it is again.
This context is as within the Yoshinkan path and you must understand that this is the martial way of Aikido. The context is as follows:
"If you look at the word "Osu" written in the original Chinese, it is comprised of two characters. The first character is "Osu", which the dictionary defines as "push". The second character is "Nin", which the dictionary defines as "Shinobu", which means endure, persevere, put up with. If you put them together you get - to push ourselves to endure any hardship, in training or in our daily lives."
"Sensei Joe Thambu also says that he feels we should look at "Osu" as saying "Please be patient with me", for both the student and teacher.
"I believe this holds the spirit of this word, and if we all carry that spirit when saying "Osu", student and teacher alike, it will pass through each and every person we train with."
I hope you can see that Osu is a word that has an important place in any Aikido dojo, as surely one thing our Aikido gives us is the strength to persevere and push ourselves through hard times and problems. Also, what better place than the dojo to learn patience and tolerance?
It is not just the word that is import, but the spirit of it. If it is just a hollow word used as nod or "Yo" in the dojo then it is worthless, but so is "Hai" or "Rei" or "Domo"!
I hope you now see why Osu is used in some Aikido Dojo and that it does have a very important place in those dojo.