A designer baby is a baby genetically engineered for specially selected traits, which can vary from lowered disease-risk to gender selection. Before genetic engineering and in vitro fertilization (IVF), designer babies were primarily a science fiction concept. However, the rapid advancement of technology before and after the turn of the twenty-first century makes designer babies an increasingly real possibility. In 2004 the term “designer baby” even became an official entry in the Oxford English Dictionary. Designer babies represent an area within embryology that has not yet become a practical reality, but nonetheless draws out ethical concerns about whether or not it will become necessary to apply limitations regarding genetically modified babies in the future.
IVF has become a progressively common procedure to help couples with infertility problems to conceive children (it is estimated 1 in 6 couples have the procedure), and the practice of IVF confers the ability to pre-select embryos before implantation. For example, preimplantation genetic diagnosis (PGD) allows viable embryos to be screened for various genetic traits, such as sex-linked diseases, before implanting them in the mother (this is a positive aspect genetic engineering). Through PGD, physicians can select embryos that are not predisposed to certain genetic conditions. For this reason, PGD is commonly used in medicine when parents carry genes that place their children at risk for serious diseases such as cystic fibrosis or sickle cell anaemia.
So here is why I think there should be limitations,
There was a case in 1996 where a couple chose the gender of their child because they already had two boys in the family and wanted a girl this was done by PGD and it did work while this case only involved the choice of gender, it raised the issues of the selection for other traits such as eye colour, hair colour, athleticism,...