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Yet on an earlier thread someone pointed out that the Sphinx' head was too small for the body, and the general consensus was that a later Pharaoh had it re-carved with his own likeness.

The face is definitely not that of Khafre, but generally Egyptologists say that it was sculpted for him and in his "living image". And it is out of scale relative to other sphinxes, which suggests that either it is really old and has been refined and recarved, or that it was something else to start with (whatever its age) and not a lion/sphinx at all. I've seen it suggested that it was originally a sculpture of Anubis. In that case the nose and ears could easily have fallen off because the stone isn't all that great.

Miroslav Verner has said that the face is that of Khufu. Since there is just one known image of Khufu (and that is about the size of a fist, with a head perhaps 1 1/4 inches in size), that's an easier position to defend (vs the idea that it is Khafre) because of the lack of other images with which to compare it. In addition, there's a New Kingdom copy of an Old Kingdom record of Khufu's having repaired the Great Sphinx, which has been cited by Verner, and by those (such as J.A. West) who favor a much older Sphinx. There is a monumental head (fragment of a larger statue, never found) which in recent years has been identified as Khufu, but without further examples (especially those with a cartouche), there's no way to verify it.

There's also at least one advocate that the Sphinx bears the likeness of Djedjefre, elder son and successor of Khufu, and predecessor of Khafre. Since there there's only one (if memory serves) suspected image of Djedjefre, that's easier to defend than the idea that it's Khafre. :')

The Dobecki et al study of the subsurface weathering around the Sphinx suggests to Schoch that the rump of the Sphinx was carved out much later than the area in front of the Sphinx, perhaps thousands of years earlier. That's a bit of a problem for the argument that the Sphinx is out of scale, because if the rump was carved out later, then it wasn't a lion (or a dog) in the first place -- at best, we can only say we don't know what it was when first carved.

It seems to me that chipping off old plaster and re-frescoing was a much easier job for Khufu's apple polishers...

Since the pyramid was built for Khufu, they saved the first step of that. There's simply zero evidence (real evidence, such as inscriptions) that the pyramid was built by someone else, or dates from a much earlier time.