Pre-Post-Scriptum: Sorry, this one got long, but I believe details should not be omitted here for a clearer view of the whole idea
I may be new to chameleons on the practical side of the subject, but cross-breeding is a debate I often had with the Phelsuma species, subspecies and color variants as well. Unfortunately, these day geckos are seldom referenced as far as the color variant's origin is concerned (geographic or habitat-related variants), but the problem is similar considering the subspecies, and there are quite a lot. Interspecific crossings are also possible on some phelsumas, discouraged by most for the same reasons I cite hereafter.
As far as pure genetics are concerned, if the cross-breeding happens between subjects of the same species and subspecies, genetic deterioration is less probable. But as those color variants are each endemic to a certain geographical area and further genetic studies are rare to inexistent (at least as far as I could google them and run them through the biology version of SciFinder we have, which combs through certain specialized journals and publications) , it cannot be excluded, and it is even highly probable, that they should deserve the attention subspecies get. Phelsuma lineata has 5 subspieces - at least - which are mainly color and habitat distinctions.
Therefore, a cross-breeding, more exactly heterosis, as the crossing is intended to enhance visual effect, color schemes, and patterns, can be potentially harmful, as subspecies have subtle genetic differences. Hence the danger of risking the rarefying of a subspecies, generating genetic disorders - most commonly, sterility, though this is more frequent with crosses between distinct species, say Bradypodion and Frucifer for example, theoretically speaking.
As color schemes are related to many a factor, including pigment cells, skin cells, pigment "vessels" in the skin layers, cross breedings can affect those natural traits with adverse effects closely related to those cells: skin defects, melanoma, over- or under-pigmentation, lack of one of the three main pigments, lack or malformation of the pigment "vessels".
Genes are stored in a twisted way on several different chromosomes for close, or seemingly close, proteins. Therefore, a genetic mutation induced by crossing species that are not meant to be can affect other systems as well. A simple example is the Stop Code, a three-nucleotid code found at the end of a gene that tells the organism, "hey, here is the end of the current protein you are producing, the genetic code after that one is gibberish" - there is a Start Code as well. A single nucleotid change - a minimal part of a gene sequence - can induce miscoding and production of useless, damaged or harmful proteins.
This is a worst case scenario, but as the boyscouts say, always be prepared.
Another aspect of mother nature is that it can be possible, but if it does not occur in nature, there is a reason. Either geographical separation of ancestors due to tectonics or deportation or migration; or darwinian elimination of weaker or unviable specimens and lineages.
Cross-breeding has been used in the past, resulting in the various horses bred for speed, build, strength; the different types of sheep or cattle for the obvious reasons of meat, skin and fur, they had specific goals. Go try to find a "wild cow", though some farmers desperately try to keep "old" bloodlines for the sake of preserving the primary variants.
Dogs are also a good example of excessive cross-breeding of a few different variants of "proto-dogs" over a couple of thousand years only.
By trying to improve a characteristic in unnatural conditions (there I mean, no predators, few if any diseases compared to nature, no competitors for food or reproduction, easy access to food, space, hideouts and partners) we would risk the following:
-hidden genetic disorders - that may or may not be harmful, but that further "weaken" the bloodlines by hiding dormant mutations, especially if the colors of the cross-bred animal are welcome by buyers.
-appearent genetic disorders - there again they may not be harmful, but if the colors are remarkable, the disorder will be inherited during further breeding
-sterility - at least there is no risk with contamination of bloodlines there, probably the best-case scenario in my point of view as it can allow for both cross-breeders to be happy without fear, and to study the behavioral differences in a sterile male or female, alone and in community. sadly, the purpose of keeping the species alive and breeding them is not at all a reality in this case
-diminishing the breeding capacity of pure bloodlines, thus diminishing the number of different genepools in the same bloodlines, and reducing genetic variety inside a bloodline. This risks what I would call "incest contamination", genetic disorders due to the very restricted family tree of the subspecies.
-ethical considerations: do we really want to turn our wolves of chameleons into chihuahuas and shi-tsus for our personal satisfaction? the same experiments have been made by others before, with reptiles as well as other families, and some species have been altered for less than that.
(I do not remember the name of the gecko that has almost perished in the attempt of providing more females for reproduction. Breeders got in a low temperature incubation frenzy to get only female hatchlings, and the female population, rare before as they died gravid in transportation or shortly after purchase, almost wiped out the male population. Similarly, a parthenogenic species has suffered greatly as males were hard to sell and almost disappeared of the captive populations, those geckos being capable of reproduction without mating. )
I am not keen on cross-breeding as you can see, too many errors have been made before, and we are probably the worst species at learning from others' mistakes

Yet I don't want to impose my point of view, just to add some more details and information that could help some understand why many are against it. Captive breeding induces sufficient changes and adaptation in animals to consider keeping those variations at a minimum - for their sake.
To compare, there are the few positive aspects I found:
-new color schemes - if at all new.
I personally find that the chameleons are sufficiently varied already, and there can be natural variations in normal breeding too. Patience is the way nature works as well
-enhanced physical characteristics
they are hard to obtain, and hard to observe on such small animals. and what for? we'll end up with the Pentaceros or Octoceros species at the end

very good if you have cable and satellite, quite secondary of use back in the jungles
Platys, for example, have been documented precisely so late compared to their spread in aquaria that there is only one global name for all the color and morphological variants.
The way I see it, there are more chances for these to go wrong on the long term, that chances of obtaining anything useful - I do not consider different colorations as useful

I am more afraid of obtening a Superchamaeleo multimixans with a prime number of horns and the latest Gucci patterns on each side - or more realistically even weaker and harder-to-breed animals - than anything "good" or not harmful turning out of this experiment.
But I stay open to debate, as my predecessors on this topic. For instance, I would consider accepting the possibility of useful, or non harmful cross-breeding, with genetic control of each resulting generation - this would mean a widespread analysis and referencing of the present populations, wild and captive, to assess genetic derivation due to crosses, but there again I don't see other purposes than visual happiness of the breeder
I think the scientist spoke out of me this time
I consider terrarium-freaks as myself to be helpers, trying to breed species to keep them from extinction, to study their behavior, their adaptability, to know the most we can about them so that, if there is one day a need for repopulation, we can be prepared to offer our best knowledge and some specimens that have not really changed. Our hobby and passion can also help reduce captures and exportation of wild specimens, which could save them as well. These are my priorities.
I suggest some read-up on the keywords heterosis, F1 hybrids, as complements to this thread. Don't exclude documents referring to other species, as those questions - and sometimes, experiments - were raised in other circles as well. The basic debate is the same though.
Al