I believe that competition, in Aikido, even as described above, is still a bad thing. Competition is about winning, IMO, and if someone in an Aikido dojo tries to "compete" with others, the results are disasterous. Uke comes in with an attack, and BOOM! Nage wants to show everyone his technique is soooo good (competition) and throws uke with excessive force, breaking his wrist.
Now, this is an exaggeration of course, but as O-sensei said: "There is no attack. To be attacked is to lose." So therefore, if we try to attack each other (competition), we both lose...