Why not use 1080p cameras for both front and back cameras on an iPad?
It's pretty much impossible to answer this without inside information, but it's likely some combination of size, cost and part availability constraints.


Size: it's hard to tell from the iFixit photos the depth of the components, but that's almost certainly the limiting factor. That's often cited as one reason the iPod Touch doesn't have a better camera (it's simply too thin). The iPad is obviously thicker, but it's still fairly limited in depth (which seems to be the most significant dimension of the camera modules).
Cost: I'd put less stock in this one, but iSuppli's estimates put the iPad 3's cameras at around $12, and the iPad 2's around $4. If we assume most of that difference is in the upgraded back camera, we can make a rough guess that it would cost about $8 more to put in a better front camera. Apple makes ~30% margins, which is about $150 on the 16 GB WiFi iPad 3. So an extra $8 would eat 5% of their margin (less on the more expensive models). I'd say that's unlikely to stop Apple from doing it if they felt it was a good idea, but enough that they wouldn't just stick it in there on a whim either.
Parts availability: Apple ships huge quantities of iPads (17 million last quarter alone, more than 84 million to date), and new models have been supply-constrained (i.e. they can't make enough to satisfy all orders) for months after launch. Requiring twice as many of a part could have detrimental effects on production (and therefore sales and profits).


I don't think any single factor is the reason why, but if I had to put money on it, I'd say it's mostly component size and availability.

One final thought: the front camera is mostly used for FaceTime and the odd self-portrait. FaceTime quality is mostly a function of the quality of your internet connection—adding a better camera wouldn't necessarily make an appreciable difference, based on my experience with FaceTime.