See no reason against it, also the truth is that neanderthals didnt "vanish" they got mixed with us, there is a lot of their dna in most modern people, its less "went extinct" more "got assimilated by the borg" erm, us.
Would be quite interesting, however i am sure we as a society still have many crap to deal with before using resources on novelty, then again as i said, we might learn something...
Hope it is treated humanely if it is done though
Mules are the of spring of horses and donkeys, they cannot produce offspring
There are no recorded cases of fertile mule stallions. A few female mules have produced offspring when mated with a purebred horse or donkey. Herodotus gives an account of such an event as an ill omen of Xerxes' conquest of Greece in 480 BC: "There happened also a portent of another kind while he was still at Sardis,—a mule brought forth young and gave birth to a mule" (Herodotus The Histories 7:57).