This isn't really an opinion, rather, a question that I thought would be relevant.
This is under the assumption that color morphs in itself are not detrimental to the health of an axie in any way, and that it is common sense mutations such as pinhead are. In theory, couldn't inbreeding be an excellent way to purge deleterious alleles from the gene pool, provided that the necessary culling is performed (removing from the gene pool, not necessarily killing). Diversity hides issues, whereas inbreeding brings them to light, allowing for the removal of the gene. With that being said, couldn't color morphs, no matter how inbred, be healthy if not even healthier than a diverse wild type, provided responsible breeding takes place?
Theoretically, you could breed specific deleterious genes out through an endogamous scheme, yes, but this is neither happening nor is it likely to happen at all. This was done with certain strains of laboratory mice (for research recquirements) and although it worked to eliminate the vast majority of recessive deleterious genes, is not without its consequences. Some strains have high incidences of tumors in late age, most commonly used strains are all albino, which is fine when you are kept in labs where even light levels are controlled, but not great when you are exposed to normal/high levels of light, and the most relevant of all, the genetic variation is extremely low making the entire strain very vulnerable to pandemics. Contagious diseases can cause massive deaths.
So yeah, it could be done, and there are specific colour mutations that are not necessarily deleterious, but the thing is, this is not happening AT ALL, it´s not likely to happen and in fact it´s happening the other way around, where the inbreeding is being used to fix and perpetuate mutations, deleterious or not, and not to eliminate mutations, ever...
So let´s not forget that even if axolotls where to be inbred to eliminate deleterious mutations, that itself has its own consequences, and that doing this would require a great deal of money, lab facilities and the elimination of all known deleterious alleles, wether they make the animal pretty, unique, or not.
Regarding your final sentence, Jasper, no, they wouldn´t be healthier. That technique can be applied to colour mutations and to wildtypes, but an albino for example, even if recessive deleterious genes are eliminated from their gene pool, will still be an albino, which even though most people wouldn´t care at all, is still an animal that shouldn´t be exposed to normal light levels.
It´s a nice hypothetical, but it´s not the solution to all the problems the current breeding systems are producing and will produce.
Antgarner, i don´t know about the mutation you are trying to isolate (provided it´s possible), but let me give you a small warning. This idea of " merely a colour gene" is insane. A mutation that causes a variation in colour phenotype can also cause very serious trouble elsewhere. The example has already been used in this thread of the spider ball python. This is a reduced pattern mutation that causes an obvious and very sought after phenotype but also causes a lack (or perhaps the mechanism is different, it´s not clear) of certain neuromelanins which in turn produce a neurological pathology called "wobbling". The same type of reduced pattern mutation that affects neuromelanins exists in jaguar carpet pythons and enigma leopard geckos, with similar neurological effects.
You can´t just assume because a mutation causes a colour variation, that´s all it does. It could be associated with other deleterious mutations, or be deleterious itself. There are albino mutations that increase the incidence of spinal kinks or cause reduced fertility, leucistic mutations that cause deafness, melanoid mutations associated to craneal deformities, etc...
It´s dangerous to pretend that colour mutations can´t be atrociously negative for the individual. It´s also dangerous to pretend that because such things haven´t been identified in axolotls yet, they won´t happen.
I´m very glad to see people reacting apropriately to animals with deformities, diminished life quality, etc, as it should be, but it would surprise all of you how much people are prepared to ignore or tolerate in favor of other characteristics, and without apparently giving it a single thought!
I also wish people would realise that this idea that as long as you just toy with the colours and nothing else, nothing bad can happen, is simply not realistic in any way.
PS: As one of the volatile individuals, let me apologize for my part in possibly spoiling the thread for some of you.