Re: Objecting to "Traditional Respect"
The relation to combat is for training of a certain mentality...and what is wrong with combat anyway? One can not grow without some element of risk...something difficult and hard. That is the most practical aspect of Budo and, for me, Aikido. I don't train hard for the sake of having "impressive" throws...nothing I do on the mat is impressive, just a figure of speech;o)...or self defense (honestly, how many fights does one get in everyday?)...but rather to train a certain mentality of spirit.
As others mentioned, bowing too low is disrespectful in that its kind of like being cocky....or mocking. I like to bow with very correct posture, straight back, eyes 90 degrees perpendicular to the spine (ie, not arching the back or bending the neck)
My dojo in Windsor actually has no Kamidana (aka kamiza) due to the diverse cultures and religions in the city. We don't associate religion with aikido (and, indeed, Shinto really isn't a religion in my eyes)...but the initial perspective to folks 'off the street' is some sort of deification toward O'Sensei/Shioda etc...
Bowing, to me, is a way to mentally clear myself of all things not training. In my group, we say "Osu!" when bowing (sometimes) which is basically form the word "to push" (yes, there is debate on this) with the idea being to push away all things unimportant to training. One of our senior teachers, Yamazaki Sensei (iai and karate), is very sociable and friendly, but if you are on the mat with him and start speaking of things not related to training, he will politely bow and ask you to come off the mat and continue the conversation elsewhere. While some may think this extremist, I think its really cool (I don't practice it though, but have respect for that mindset).
I don't know if I'm allowed to post other's published work on here, so I will err on the side of caution, but there is a good article/chapter entitled "Rei: Ettiqute" on Chapter 35 in the book Sword and the Brush, by Dave Lowry that discusses this very subject.
Lowry, D. (1995). Sword and the Brush. Boston: Shambala Publications, Inc.