The issues are so interconnected that I'm having a hard time pulling them apart to explain them*. One issue is the descent of GFAJ-1 from ancestors that used phosphorus and not arsenic for metabolism and for nucleic acids. Another is the numbers of genes and proteins that would have to be different if a cell used arsenic in place of phosphorus. Another is the selective advantage of using arsenic in an environment with abundant arsenic and little phosphorus**. In my attempt to explain these I'm going to ignore the metabolically devastating instability of arsenic-ester bonds.
All known organisms need phosphorus to make DNA, RNA, ATP and NADP, and many metabolic reactions either require addition of phosphate groups to small molecules or act on molecules with attached phosphates. Phosphorylation also regulates the activity of many proteins. Thus a cell that used the same basic metabolic pathways but with arsenic rather than phosphorus would need to have arsenic-specific versions of all proteins that interact with any of these molecules. Because phosphorylation is so ubiquitous, this is likely to be at least half of the proteins in the cell. This means that full replacement of phosphorus with arsenic could not have arisen in a single step, because replacement requires changing so many different genes.
How could it have arisen? Because GFAJ-1 is a member of the known biosphere, we need to start with an ancestor that had conventional phosphorus-based metabolism. Because just about all cellular phosphate enters the system by way of ATP (if I remember my biochemistry correctly), the simplest way (perhaps the only way) to begin using arsenic would be a mutation in an enzyme that attaches free phosphate to a metabolite. I'm thinking of an ATP synthase that normally puts inorganic phosphate onto ADP to make ATP. But this hypothetical arseno-version of ATP would only be useful if other proteins could use it. Initially it's more likely to be toxic to all the normal proteins that interact with ATP and with phosphorylated metabolites. The number of mutations required to adapt this many proteins to tolerating arsenylated versions of their substrates would be prohibitive.
We can separately consider the magnitude of the selective benefit that would be achieved by replacing phosphorus with arsenic. In an arsenic-rich phosphorus-limited environment, complete replacement of P with As would give a large competitive advantage (all else being equal). However, an organism that replaced only a small fraction of its phosphorus with arsenic (as is now claimed for GFAJ-1) would obtain only a proportionately small growth advantage over cells entirely dependent on phosphorus. For example a cell that replaced 1% of its P with As would still need 99% as much P as its competitors. A bacterium could achieve the same advantage much more easily by a 1% improvement in the affinity of its phosphate uptake system.
A 1% selective advantage certainly isn't trivial, and, all else being equal, a mutation causing this advantage would be expected to take over a population. But all else isn't equal if the advantage comes from substituting arsenic for phosphorus. Rather, replacing a small fraction of the cellular phosphorus with arsenic creates even bigger problems than replacing all of it. That's because the proteins would have to be able to use both phosphorylated and arsenylated substrates
I think the paper's authors may have been led astray by their initial hope that GFAJ-1 was a member of a shadow biosphere that used only arsenic (not phosphorus) for all of the cellular processes that members of the known biosphere use phosphorus for. Such a cell would have an integrated arsenic-based metabolism and, if we set aside the chemical stability problems, its recent evolution would be no more problematic than that of phosphorus-based bacteria. However, once GFAJ-1 was discovered to be a member of the known phosphorus-based biosphere, the authors may not ahve rethought how it could have evolved to have the arsenic-using properties they are attributing to it.
* I suspect the difficulty I'm having in clearly explaining the problems isn't a writing problem. Instead, it's caused by the many intrinsic contradictions that arise when we consider how GFAJ-1 might have evolved to use arsenic.
** Mono Lake, the natural environment of GFAJ-1, has abundant phosphorus (400 µM) and arsenic (200 µM).