“The only specific suggestions that I could find was because of the DNA replication process and…”
No. The explanation can have nothing to do with DNA replication. If the structure does not exist, you can’t replicate it, if it does, Nature will evolve a mechanism. (The related SE question, mentioned by @Gilleain, asked whether it could still replicate if it were parallel, i.e. using the enzymes that have evolved for parallel DNA.)
I know that parallel DNA helices exist…
Let us clarify this first. Perhaps the most extensive parallel duplex DNA, the structure of which has been determined, is that described by Parvathy et al.. The two parallel strands of this are shown below:
The following points should be noted:
- This parallel DNA (and the shorter examples that preceded it) is not a pure stretch of complementary base pairs.
- It is stabilized by what the authors refer to as “CC+ clamps” at either end. One is left to conclude that without these the duplex would not form.
- All the complementary base-pairs are of the type AT (actually reverse Watson–Crick base pairs). Presumably GC base-pairs would have destablized the structure.
(You can inspect this structure in three-dimensions here. Choose ‘Licorice’ style and colour ‘by chain’ and notice the non-planarity of the three base ‘pairs’ at each end.)
So although the question refers specifically to parallel DNA helices with Watson–Crick base pairs, it should be recognized that extended parallel DNA helices composed of any kind of complementary AT and GC base pairs are not found, and the question applies equally well to them.
“In the diagram if we were to flip one of the strands while keeping the other same, hydrogen bonding is still possible”
The diagram in the question is two-dimensional; DNA is three-dimensional. It is only by considering the three-dimensional structure of DNA can you approach this question.
So how would one do that? One must consider the free energy of alternative structures in the relevant millieu to determine which will occur (i.e. be more thermodynamically stable).
This will tell you whether single DNA strands with parallel sequences will form a double-stranded (ds) structure or not.
This will tell you whether ds-parallel DNA is more or less energetically stable than a ds-antiparallel DNA. Hence, even if both can form (which I doubt, without some special circumstances*) the lower thermodynamic free energy of the anti-parallel dsDNA would give organisms adopting it an evolutionary advantage.
And the answer to the question?
It seems unlikely that one single factor is responsible or it would have been pointed out in elementary text books such as Berg et al..
To answer would require a complete theoretical analysis of the structure or structures. First one would have to build a model of a proposed parallel structure that could accommodate Watson–Crick base pairs. This in itself is a problem because there are likely to be many alternative structures. Perhaps there are computer programs that can find the structure with the lowest energy. This would be calculated in the classic manner, calculating the positive contribution of hydrogen bonding (which depends on distance and angle), ionic interaction etc.* against the negative contribution of charge and steric repulsions.
*Etc? The two-dimensional diagram fails to consider the contribution of base stacking (how could it?), which contributes to a considerable extent to the stability of nucleic acid helices, as the original cover design of Stryer’s Biochemistry is a constant reminder: