Wow... This thread is a map between spark and powder keg . *grins evilly*
Would you be willing to share your knowledge by explaining the context of competition and adding your opinions of the pros and cons of competition/cooperation?
I've already done this several times before and once in this very thread.
However, here it is again. A teacher can teach the basics of his/her art. It is up to the student to take those basics and make them his own. For example, a student learning how to draw manga character must first learn how to draw circles, squares and all other basics of drawing. A teacher can teach him how to do this. What the teacher cannot do, is teach the student how to make those basics his.
In other words, a teacher can only show the way, it is up to the student to follow it.
Aikido is the same thing. Nariyama-shihan cannot teach me how to do randori. He can teach me the basics of kata. It is my task to make those kata mine. This is why I do randori. It is teaching me to make Aikido mine. It is forging my Aikido. Hence whenever I "compete" in Aikido, I am always winning. Best of all, my Uke is winning too. We are both winning in harmony. This is why what we do is called Aikido.
Now, could the same thing be achieved without "competition"? ... This is a meaningless question. It's down to semantics of what you understand by competition. Not even a dictionary definition will help. It's a matter of preferences and view point. Hence this is why I suggest that you visit other Dojo from different styles. See for yourself with eyes unclouded -- A great prise to however can tell where the quotes come from.
Does that help?