You build a mountain in your effort to explain a shadow.
I agree with your initial postulate that points tend to move the training into the realm of sport, but then you abandon that, saying that competition is in everyday life and also in our kata training.
I say that if you call something like tomiki style tanto randori a "competition," with full knowledge of *all* of the connotations that word carries, you deserve every "misunderstanding" that that word generates. But are people really misunderstanding? I submit no, but must make one point first.
You say that in any encounter, there may exist some competition, using the example of if you time your drive from point A to point B and fail to meet your goal, "are you a loser?" Your use of the word "loser" here is obsequious and inflammatory, causing every person of any self-esteem at all quickly to reply, "No, not me! I'm no loser!" But people are not running to agree with you in that statement, they are running away from the connotation "loser" has in our culture. Complete honesty would have called for a comparison such as this: if there is competition in my drive-time, then there must be something I am competing against, otherwise there is no challenge and no reward. (One of my instructor's describes a fight the same way - it's not a fight until both people say it's a fight; until then it's just a pick-on). So what was I competing against in my drive? Most basically, time. If I get there ahead of schedule, I win. If I don't, time wins. In that contest, I am the loser; I am not "a" loser, with the connotation you casually employ.
So, back to my question, do people really misunderstand? I don't think so. We are aware that competition can be friendly and that there is competition in every day activities (with so many people pointing it out on this thread, how could it be otherwise?). However, we are also aware that as soon as points are awarded, the focus shifts *onto* the competition. And in an activity such as tanto randori (the tomiki definition), that shift in focus, along with the points, turn it into sport rather than art... rather than budo.
But just so that we're all clear, I don't care if someone wishes to train that way, I just want them to be honest that what they are doing is sport. My questions don't come from a loathing of competition in aikido, but from a desire to learn what benefits people get from it that I don't get from my normal training. I'm looking for something that will make me want to include the tomiki style tanto randori (or other similar competition events) in my daily/monthly training.