The reason so many experienced people suggest learning the basics of Vim (or, in my case, Emacs) in one go is because it works quickly and efficiently--certainly more quickly and more efficiently than an incremental approach. Additionally, just giving up on arrow keys and the like does not necessarily entail a "huge volume" of memorization.
I am an inherently lazy person; I cannot just sit down and memorize stuff (one of the reasons I'm in CS). Yet I definitely support giving up the mouse and arrow keys immediately.
When I originally picked up Emacs, I went through the tutorial and promptly forgot exactly which keys did what. However, I decided to follow the tutorial's advice and learn how to navigate properly. To do this, all I did was not use the mouse or arrow keys for editing some text. For the first couple of days, I had to keep looking the keys up each time I did anything; later--relatively abruptly--I started using them without realizing. There is no way I would have learned nearly as much as quickly if I had not got through a couple days of not knowing what I was doing.
Once the standard moving commands became second nature, I started using some of the more specialized ones (like moving around by line or paragraph or expression). Without having given up on the arrow keys and mouse, I would probably never have learned the more advanced movements which are now exceptionally useful.
Basically, to follow your suggestion would be to avoid a couple days of bumbling around in favor of being less effective for a very long time. On the other hand, with my approach, I did spend a couple days being incompetent but then the bindings became natural. Ultimately, to me, being lazy involves not just minimizing work immediately, but increasing efficiency in the long run as well.
As a contrast, I know many classmates who have tried to learn Emacs your way. Most of them can use it, but not much more efficiently than notepad; I regularly see them spending minutes doing menial tasks that would have taken seconds had they known Emacs better. In the context of a 90 minute lab, that is not trivial at all; even in the context of working full time, the amount of time they can save should not be ignored.
Ultimately, all it takes to learn Emacs (and, I imagine, the same can be said of Vim) is a little bit of patience and willingness to embrace change. By jumping into the deep end immediately, you can learn really quickly, and reap the benefits almost immediately.