Why ambidextrous persons are so rare?
While not specifically answering why ambidextrous persons are rare, one potential explanation is that mixed-handedness and/or ambidexterity seems to be related to adverse effects. For instance, some studies have shown that mixed-handedness (which might not be exactly the same as ambidextrous, depending on how you define the terms) is related to ADHD symptoms (e.g. Rodriguez et al. 2010) and patients with schizophrenia have an overrepresentation of mixed-handedness (Green et al, 1989; Orr et al, 1999) and ambidexterity (Crow et al, 1996).

A potential reason for the adverse effects seems to be that mixed-handedness and ambidexterity is related to delayed or weakened dominance of one cerebral hemisphere, which is important for language development (see e.g. Crow et al, 1996). See also this quote from Intelligence and the ‘Intelligence Quotient’ (Crow, 2001 from Encyclopedia of Genetics):


  Handedness, reflecting cerebral dominance, is a trait that is associated with quantitative variation. Whether this variation is a correlate of human cognitive ability, as would seem plausible if it underlies the specific characteristic of language, has been much debated, but it now appears that lesser degrees of lateralization (‘hemispheric indecision’) are associated with delay in the development of verbal, and also nonverbal, ability (Crow et al., 1998). Thus it appears that lateralization is associated with significant variation in the rate at which words acquire meaning, and that this variation reflects a dimension that is specific to Homo sapiens. 


This is not my area of expertice thought, and others more knowledgeable about the field can maybe expand on this or explain more in detail.