I have also noticed that some of my T's would eat all or some off their Exuvia ... I always amused that it might be because they have not eaten while in premolt, since they might be hungry... But I have noticed that the Brachypelma species I keep, are more likely to do so than the Poecilotheria in my collection... so the theories in the previous comments might be more on the mark.

I have also heard that it can be detrimental to a T's to eat its own exuvia...

Maybe the more experienced members can elaborate on this and I'm sure that Stan has some useful info for us on this topic.

I have never had a spider eat (consume) its moult before (And not sure they would eat the whole moult either).
I have often had them "chewing" on their moults though, especially the abdominal side of the moult.
That being said, some spiders like my P.muticus shred their moults into tiny little pieces and compact them into the burrow walls. Maybe this is why you think the spiders "eat" their moults?