Well, see, you've just defined the terms of the argument and thus constrained the only possible answer to being the one you want. If training is indeed "the most important part" for someone, by definition, bowing or not bowing is a secondary consideration. But for someone who is considering training, who does not currently train, it is probably not "the most important part". If religion doesn't make sense to you, think about family obligations: someone wants to train but is responsible for the care of two young children. It would be a bit odd to expect training to be "the most important part" for this person, certainly not as they're just approaching aikido for the first time. Very few people have the luxury of setting all other considerations, obligations and principles aside in order to train; by far the majority of us who do train, still are accountable to these other considerations. Restrictions caused by matters of principle are surely as real as those caused by practical life obligations, don't you think?
Religions does make sense to me. Served as a missionary for years. Putting off having children so my body is in condition. My mother understands why I don't call a lot. <3
It isn't a luxury, it is a sacrifice. I'm accountable for other obligations, Aikido complicates other engagements, it's just worth the complications. Sort of like dating some one your mom hates.
Like anything, you can't get something for nothing. You will grieve the sacrifice of friends, or family, or free time, or job offers...but it has to be worth the sacrifice to you. It has to be worth grieving that sacrifice too, which is often harder than the initial sacrifice.
I will admit it however, I'm approaching the situation from a different mind-set. And if one think in your life is more important than Aikido, to the point it makes Aikido unpractical, then you must sacrifice Aikido and grieve that loss.
Personally, I never cared if some one bowed or not..so long as they were respectful, and a light-uke.