Given enough time and effort one could get a wolf like dog from a beagle. None of the changes in DNA are irreversible. And Neanderthal were Homo Neanderthal not Homo Sapien. They were a distinct and separate population.
You and i are just going to have to disagree.
If a population is homozygous for a gene or series of genes it cannot produce the absent trait. Ie blue eyed parents cannot have brown eyed offspring.
The reduction in the variation of the Canis genome that yields ‘Beagles ‘ means that Beagles’ lineage cannot be bred to make wolves (morphology ) because those genes are not in the Beagles’ chromosomes.
Sans ‘magic’ mutations in the genome of course.
Taxonomy is a human construct not a genetic one.
On mobile pardon any errors.