I think it is a good thing to practise various attacks and techniques at random in randori. I consider that very education because nage discovers his or her strong and weak points. You automatically turn to the techniques which is most natural for yourself, and even more important, find out which technique you have to work on (very, very much). However, this is not competition, you could call it sparring but I consider it basic training.
Competition is when 2 (or more) people come together in a predesignated limited space and start hurting each other untill one of them gives up (voluntarily or compulsory due to serious bone damage).
First of all IMHO aikido cannot be conducted in a predesignated limited space. It is everywhere (in your movement in day to day life) or you are doing something that is not aikido. You come together with fellow students in a dojo (all dressed up and with your boken, jo etc.) to further your own development and discover more about yourself.(Face it, it looks funny if you go around wearing gi and wooden weapens 24 hours a day
Secondly, I don't think aikido is meant to hurt, you try to convince your PARTNER that a certain movement is not benificial for his or her general healt by applying a certain amount of pressure. Depending on your partner the amount of pressure can be increased or reduced depending on his or her level and ability to take ukemi.
In my dojo you are in big trouble with our teacher if your partner gets seriously hurt (nobody minds a bruise, some tense muscles or some sprained tows or fingers, but as soon as a docters apointment is advisable....) But in the years I have been training no real serious injury occured.
Finally, our teacher says if you hurt uke too much he does not want to train with you anymore and you cannot do aikdo anymore. Competition = hurt and therefore not aikido, training in predesignated techniques or at random is trying to better yourself and your partner, without any semi-permanent damage.
Sorry for the long post but I feel very strongly about this (but you probably guessed that much). I have had serious bone damage, not MA related, and I could not train for a year. I am still not at my previous level of bodycontrol and it will probably take a couple of years more before I have overcome it all. Anybody who practises aikido and considers competition as in hurting your partner to the point where he/she gets damaged has gotten the wrong idea somewhere (sorry, I don't mean to offence any lawenforcing people here, if required, go ahead and 'convince' someone that what they are doing is wrong, I donnot mind or criticize that).
One of the beautiful thing of aikido is that everyone can practise with everyone, experienced with unexperienced, young with old, small with large and male with female. You learn different things from all these partners. Frankly, I don't even see how anyone could set up a competition, you would have to exclude a lot of people and, to me, aikido is alot about equality, I can train with anyone and I like that.
Thanks for listening to my ramblings, hope I made my point clear.