Yep
spoiled and old eggs have a higher chance of hatching mutant but also a higher chance of failing.
( you can see egg hatch chances if you click "View egg hatch chances" in your hatchery)
You can only hatch natural coloured mutants so a dye kit if the only way to chance their colour~
and mutants are rather special to some people and are considered much better than a normal natural coloured/ low coloured hatch by most ~
:)