Another possibility is that the G Y-chromosome produces slightly less male offspring than other haplogroups.
I theorised five years ago that the exceptionally wide distribution of haplogroup R1b (and in fact also R1a) was due in part to a genetic bias towards producing slightly more male children. It doesn't take much to achieve this over hundreds of generations. If haplogroup R1 produced just 1% more boys than other haplogroups in average, R1 would increase its proportion 7.4 folds after the roughly 200 generations since the presumed arrival of R1b in Western Europe 6000 years ago.
In other words, if a population was composed of 100 R1b men and 100 men belonging to other haplogroups, if R1b men fathered 101 boys each generation, but other haplogroups kept a stable 100, it would take only 70 generations (about 2000 years) for R1b men to reach 200 boys born each generation, and therefore double their proportion against other haplogroups. The R1b frequency would thus pass from 50% to 66.6%. After 200 generations (about 6000 years), there would be 738 R1b boys against 100 other boys born at each generation. R1b would now make up 88% of the lineages in that population. As you can see a very minor initial advantage can lead to enormous changes in frequencies after a few millennia. Western Europe now has about 60% of R1b in average. With a bias of 1% more boys per generation, it would have taken an initial population of less than 10% of R1b 6000 years ago to reach that modern proportion.
If haplogroup G had the opposite bias, and produced 1% less boys than men belonging to other haplogroups, its proportion would gradually decline without any other factor required. If a given Neolithic population had 50% of hg G, with a bias of -1% of boys per generation against other haplogroups, it would have taken about 7000 years for the proportion of G to naturally decline to only 5% of the population.
If we combine both the positive bias of R1b (and possibly others like R1a, some subclades of J2 or E1b1b) and the negative bias of G2a (and possibly many subclades of F, I, J1xJ1c3, and T), it would in fact take much less than a 1% bias in each direction for frequencies for shift dramatically since the Neolithic or Bronze Age.
Each mutation on the Y-chromosome can potentially increase or decrease the proportion of male offspring. I believe that this is how some haplogroups or subclades become numerically dominant in the long run, while others progressively disappear. Most mutations have no effect at all. That is why, once a mutation increasing the chances of having more male children, and therefore increasing the chances of survival of the Y-chromosome itself, takes place, the lineage can develop many new subclades without being affected positively or negatively. Some new subclades will eventually get even more positive mutations, while others will go back to a more stable male-female ratio.
I wouldn't be surprised if haplogroup G suffered such a disadvantage at first, at least until one of the mutations around G2a3b or G2a3b1 happened, which stimulated the growth of that particular branch. Likewise, widespread branches of hg I, like I1 and I2a1b (M423) probably owe some of their success to mutations conferring a slight bias towards more male offspring. Such a bias would be almost imperceptible in genealogical times (within a few generations), but significant over hundreds of generations.