There are several things wrong with it, primarily the fact that the aforementioned problematic government must administer it. But I think that a person who burns a child to death needs a different form of execution than that provided for a loving pet. Putting a murderer to sleep is just as heinous as letting him go -- if he's not begging for death at the end of the rather long process, it was done incorrectly.
Lots of problems. Better just let the survivors' family deal with it.