The following is anecdotal and rambling, but I think it goes a good way towards addressing the question (from a personal point of view).
My daughter and I play a variant of the card game War to work on arithmetic facts. Originally, we played "Addition War": we would each play a card, and the first to sum the two numbers got to keep both cards. When her first grade class started drilling subtraction facts, we started playing "Subtraction War." At one point, she turned up a 5 and I turned up a 3. She got very angry with me when I said "Oh, three minus five is negative two!"
"Papa!" said, "You can't minus five from three! Five is too big!"
At this point, I introduced her to a number line model of addition and subtraction. The story that I gave her is that a frog is sitting on a lily pad in a pond. Every lily pad has an address or number, counting up from 1, going from left to right. When we add, the first number tells us where the frog starts, and the second number tells us how the frog hops. For example, $3+4$ means that the frog starts at the lily pad labeled "3", then hops to the right four times, which takes it to the lily pad labeled "7". Therefore $3+4=7$.
(Note that this was all done on a piece of paper with an actual toy frog to hop around, which makes life a little easier.)
Once she got the idea of addition with the frog, we started playing the same game with subtraction. The only difference is that the frog now moves left instead of right. For starters, we only worked "proper" subtraction problems, where the minuend is larger than the subtrahend. I then asked about $4-4$. Our lily pads started at 1, so this didn't seem to make sense (the frog splashed into the water). However, since we are clever mathematicians, we can plant a lily seed and grow a new lily pad. She had already seen zero before, so it made sense to call this new pad zero, and get on with life.
Finally, we can introduce negative numbers. I got out a different color, and started "planting" more lily pads to the left of zero. I labeled them going up from right to left in the new color (which happened to be purple). She was really resistant to this kind of labeling at first—she didn't like there being two different "3s", for example, but we managed to talk about "left three" and "right three", and she eventually bought the idea. After a bit more play, she got pretty comfortable with the idea of problems like "Five minus nine is 'purple four'" (or 'left four'). A few months later, she is pretty comfortable with the idea of (small) negative numbers.
Now when we play subtraction war, black cards always come first, so the "correct" difference if I play $5\spadesuit$ and she plays $6\heartsuit$ is "Negative one!" If the cards have the same color, either positive or negative answers are fine.
In any event, I think that this model of subtraction—which really is exactly what you propose—is not only appropriate for an introduction to subtraction, but is, perhaps, the "right" model for addition and subtraction in general. It might seem less concrete than "three apples plus two more apples is five apples," but I think that it gives a much more concrete meaning to negative numbers. Frankly, I still have trouble with negative quantities (negative apples scare me), but I have no problem with negative coordinates or negative directions.