Unfortunately, the regrown tail portion is all collagen and cartilage. There's no fat or muscle stores for it to provide that kind of value.

The alligator-tail paper authors point out a couple of additional pieces of information you might find interesting:

- A robust, adaptive immune system is seen as an impediment to regeneration, which could be why mammals and birds are both so rubbish at regrowing lost body parts compared to reptiles and amphbibians. In salamanders, limb loss provokes only a weak immune response and regeneration is fairly robust. In the clawed frog Xenopus, regenerative abilities are robust in juveniles but reduce as the immune system matures. Adult crocodilians have robust immune systems like birds and mammals do, and as their only tail regeneration was seen in very juvenile alligators, its possible that their underdeveloped immune systems allows them to (partially) regenerate in a way that wouldn't be possible once the full power of their adult immune system is established.

- We have fossil evidence of partial tail regeneration in the Jurassic marine crocodile Steneosaurus bollensis (unfortunately, the papers the authors link are both in German and I don't understand them). The authors (briefly) speculate that tail regeneration was something all archosaurs inherited from their reptile ancestors, but that this ability was subsequently lost in the dinosaur/bird line (again, possibly and partially because they evolved more adaptive immune systems). So rather than being a new trait that evolved in alligators, it might be a partially-inherited ability that was potentially diminished/lost in some other surviving crocodilians.