I came across hierarchies holding a single child.
While creating a consolidation over only 1 element might make sense in some hierarchies, some people just use consolidations as an alternative to aliases.
Either they just don't know they exist or they come from an age when TM1 did not have aliases yet.

The following process will help you identify all the "single child" elements in your system.
This effectively loops through all elements of all dimensions of your system, so this could be reused to carry out other checks.

#where to report the results
Report = '\\tm1server\reports\single_children.csv';

#get number of dimensions on that system
TotalDim = Dimsiz('}Dimensions');

#loop through all dimensions
i = 1;
While (i <= TotalDim);
  ThisDim = DIMNM('}Dimensions',i);

  #foreach dimension
  #loop through all their elements 
  j = 1;
  While (j <= Dimsiz(ThisDim));
    Element = DIMNM(ThisDim,j);
    #report the parent if it has only 1 child  
    If( ELCOMPN(ThisDim, Element) = 1 );
      AsciiOutput(Report,ThisDim,Element,ELCOMP(ThisDim,Element,1));
    Endif;
    #report if consolidation has no child!!!
    If( ELCOMPN(ThisDim, Element) = 0 & ELLEV(Thisdim, Element) > 0 );
      single = single + 1;
      AsciiOutput(Report,ThisDim,DIMNM(ThisDim,j),'NO CHILD!!');
    Endif;
  j = j + 1;
  End;
  i = i + 1; 
End;