Consequences

A deformation of the skull (Plagiocephaly, Brachycephaly, Dolichocephaly) that can be treated, in addition to the visible aesthetic consequences, can have regrettable consequences in the short and long term.
The more severe the cranial deformation, the greater the risks.
Numerous researches and studies on the consequences of deformations of the baby's skull have highlighted:

The first visible consequence of plagiocephaly (brachycephaly, dolichocephaly) is above all Aesthetics.
The appearance of the baby's skull changes.
Besides the aesthetics of the head of your baby, and future adult is it not important?
Most often there is a flattening at the back or on one side of the skull, with an asymmetry of the ears and sometimes the facial features change with a more prominent forehead on one side.
Skull deformations do not disappear over time without proper treatment.

(Study published on the US National Library of Medicine: LaBrie RA, Scott RM. Analysis of posterior plagiocephaly: deformational versus synostotic. Plastic and Reconstructive Surgery (1999) https://www.ncbi.nlm.nih.gov/pubmed/ 9950521)

There is still a debate between cranial deformities and children's motor development.

But studies have highlighted a link between positional deformations (plagiocephaly) and:
                  – a decrease in the acquisition of specific motor skills depending on the severity of the cranial deformation.
(Cabrera-Martos I, Valenza MC, Benítez-Feliponi A, Robles-Vizcaíno C, Ruiz-Extremera A, Valenza-Demet G. Clinical profile and evolution of infants with deformational plagiocephaly included in a conservative treatment program. The International Society for Pediatric Neurosurgery (2013) https://www.ncbi.nlm.nih.gov/pubmed/23644628)

                  -a lower score on the infant development test (BSID-III)
(Brent R. Collett, Elizabeth H. Aylward, Jessica Berg, Candice Davidoff, Justin Norden, Michael L. Cunningham, Matthew L. Speltz. Brain volume and shape in infants with deformational plagiocephaly. Child's Nervous System (2012) https: // link.springer.com/article/10.1007/s00381-012-1731-y)

It has been shown that cranial deformations are linked to an increased risk of developmental problems with an increase in the school age for specific care: language problem (speech therapy), postural problem, etc.
(Robert I. Miller, Sterling K. Clarren. Long-Term Developmental Outcomes in Patients With Deformational Plagiocephaly. Pediatrics (2000)
http://pediatrics.aappublications.org/content/105/2/e26.short)

A study concludes on a probable link between a deformation of the baby's skull (Plagiocephaly) and scoliosis.
We find in the genesis of scoliosis certain risk factors common to plagiocephaly.
(Saccucci M, Tettamanti L, Mummolo S, Polimeni A, Festa F, Tecco S. Scoliosis and dental occlusion: a review of the literature. Scoliosis (2011)
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3162939/)

It has been shown during scientific research on cranial deformities, that the reaction to certain auditory stimuli is weaker among children with plagiocephaly compared to children without.
(Balan P, Kushnerenko E, Sahlin P, Huotilainen M, Näätänen R, Hukki J. Auditory ERPs reveal brain dysfunction in infants with plagiocephaly. Journal of Craniofacial Surgery (2002)
https://www.ncbi.nlm.nih.gov/pubmed/12140415)

Deformations of the baby's skull (Plagiocephaly) which combine asymmetry of the face, lead to occlusion disorders and displacement of the jaw forward.
Requiring the implementation of future orthodontic treatment in children.
(St John D, Mulliken JB, Kaban LB, Padwa BL. Anthropometric analysis of mandibular asymmetry in infants with deformational posterior plagiocephaly. The American Association of Oral and Maxillofacial Surgeons (2002)
https://www.ncbi.nlm.nih.gov/pubmed/12149730)