Okay, here is where you're argument breaks down. Resolution should maintain an internal consistency. Considering resolution from on perspective should not give you a different answer than considering it from another perspective. By your argument, if there were two devices, one with a resolution of 1024x768 and another with a resolution of 1448x1086, but with the exact same physical dimensions, then you would argue that the dpi resolution of the latter device is roughly 1.4x that of the first device, while the "total pixel" resolution is about 2x that of the first device. So, now anytime you start talking about resolution you have to ask "what resolution?"
Now, the reality is that we are already using a short form for the term "resolution". In fact, up until recently, we very pointedly talked about x-resolution and y-resolution, as pixels often weren't square. More recently, we've dropped the x- and y- designations because pixels have become fairly universally square. So, when you speak of resolution, it is a short for of saying x- and y- resolution. In other words, saying "the resolution doubled" is really a short way of saying "the x- and y- resolution doubled", which, of course, gets back to the fact that we don't describe the display in terms of total pixels, but in terms of x- and y- dimensions.
In a world where pixels are square, it wouldn't be much of an issue to describe a screen in terms of total pixels. As things are, we use three numbers to describe a screen size: diagonal physical dimension, x pixel count and y pixel count. So long as pixels are square, we could just as easily use: diagonal physical dimension, aspect ration and total pixel count.
Long and short, if you understand where our language in this area comes from, it is clear that resolution is spoken of in linear pixel counts or linear pixel counts per unit distance (i.e. dots per inch, or dpi). Thus, as each of these terms doubled, we speak of the iPad's resolution, as a whole, as having doubled. Not quadrupled.
