My GTA colleague suggests that GTA may persist because of species-level selection. 'Species' is a tricky concept because these are bacteria, but we can simplify this to consider selection of lineages.
The basic idea is like that proposed to explain the surprisingly high frequency of bacterial lineages with defective mismatch-repair genes. Like most mutations, most GTA-mediated recombinational events will probably be deleterious. But some will be beneficial. Each time a beneficial recombination event occurs the lineage of cells descending from it will all contain GTA as well as the new combination. Provided the short-term and long-term costs of GTA don't cause the new lineage to go extinct or lose its GTA genes before the GTA-mediated beneficial change, lineages with GTA could take over.
Evolution-of-sex theorists have produced theoretical evaluations of such 'hitchhiking' processes, treating the allele in question as a 'recombination-modifier' (in this case the 'allele' would be the block of GTA genes). I haven't looked at the literature recently, but I think the general conclusion is that hitchhiking is common but weak; it is very unlikely to push an otherwise harmful allele to fixation. But these analyses weren't done for bacteria but for sexually reproducing eukaryotes, with the modifier controlling the frequency of meiotic crossovers between two other loci. I don't know how they would apply to bacteria.
Nevertheless, we know the ability of relatively rare beneficial events to preserve the GTA gene cluster must depend on how frequent the beneficial events are, how beneficial they are, how often GTA genes themselves undergo mutations that block their function, and how much (if any) harm the GTA genes cause. For example, if beneficial events are very rare, functional GTA genes may be lost by random mutation in the interval between beneficial events. Subsequent selection might cause the lineage to then go extinct, but it wouldn't bring the GTA genes back.
The important question is, how could we tell if this sort of thing is responsible for the persistence of the GTA genes? Short answer: I don't know.
12 hours ago in Variety of Life