What is the secondary structure distribution per AA in the Human proteome?
The question asks why the distribution of coil, alpha-helix and beta-strand is 60:30:10 rather than 33:33:33. The answer is: 


  “Why not”


This is because there is no reason whatever to expect that three types of structure (or in the case of coils, lack of structure*) should be present in equal amounts in proteins. It is like expecting that the percentage intron, exon and ‘junk’ DNA should be equal, or that the percentage of fuel reserves stored as glycogen and fat should be the same. Yes, they belong to the same category, but they are sufficiently different in each case for one not to be surprised if they are not required in equal amounts.

To understand this one needs to look a little more carefully at the occurrence of alpha-helix or beta-strand conformation in the three-dimensional structure of proteins. Three points may be emphasized:


Amino acids have particular conformations because they are part of an extended helix or sheet of strands the entirety of which leads to its structural stability — you don’t have a random mixture.
In many cases the helices or sheets are occur in particular combinations to give a family of proteins of similar overall structure. Again, the idea of random mixtures doesn’t enter into the equation.
These overall structures are suited to particular functions, so the abundance of proteins from a particular structural family will be determined by the requirement for antibodies or ion transporters or signal transducing proteins etc., not by some shake of the dice.


Images illustrating two such families are shown below:



(a) shows an ion transport proteins, predominantly alpha-helices, whereas (b) is an immunoglobulin domain with a distinctive pattern of beta strands (as well as some helix). For further examples and information I suggest the EMBL on-line course on protein classification and Berg et al. online, for example Section 7.3.

*Footnote 1: Situations where equal occurences might be expected
It is worth while contrasting the situation with protein secondary structure to some where the prior expectation might well be for equal usage, and the deviation from this could be regarded as bias and an explanation worth asking for:


The different proportion of the 20 amino acids in proteins (although a chemist would not expect equal proportions)
The different usage of synonymous codons of the genetic code in various species and mRNAs
The different usage of the similar molecules with a high phosphoryl group transfer potential: ATP, GTP, UTP and CTP (often loosely termed ‘high-energy’)


*Footnote 2: A coil is not a secondary structure

As is stated in the Wikepedia entry for Protein Secondary Structure:


  The random coil is not a true secondary structure, but is the class of conformations that indicate an absence of regular secondary structure.


It might be mentioned in regard to protein structure that there are smaller three-dimensional motifs that the analysis quoted does not consider. These do not occur in equal proportions either, to nobody's great surprise.