Many native Georgia residents tell me that it's a state constitutional requirement.
The "constitutional requirement" story is a myth according to this lengthy but interesting explanation of why only Texas has more counties than Georgia. According to the history, not only is the "constitutional requirement" a myth, but "convenience of the people" is generally a myth, too. Georgia has so many counties because of politics and political spoils.
Georgia had only 89 counties in 1835. By the 1870s, there were 137. Splitting an existing county or counties to create a new county merely required legislative vote in those days. According to the article I linked above, the creation of new counties was often for political spoil:
In some cases, influential legislators from a “lesser city” were able to divide their county in two, making their hometown a prestigious new county seat. New counties also meant a slew of new jobs, not just for sheriffs, deputies, judges and clerks, but jobs for constructing new government buildings, running telegraph stations and the like. County seats also attracted railroads, which meant hotels and taverns and shops. Since Georgia was largely rural at the time, a new county could also bring things like police protection and court services much closer to home.
Sometimes petty squabbles were involved: when the voters of Clarke County voted to move the county seat from Watkinsville to Athens, miffed Watkinsville residents created Oconee County so that their city would remain important.
It wasn't until 1877 that the Georgia Constitution froze the number of counties at 137. Then there were a couple of constitutional amendments to increase the number of counties. Finally, during the Depression, almost-bankrupt Milton County and bankrupt Campbell County voted to merge with Fulton County.
But I digress, and Georgia has 159 counties, second only to Texas's 254.
Perhaps Georgia has as many counties as it does perhaps more because of a system of political spoils than to make things convenient for farmers and other Georgia residents.
Your summary is quite probably so. In any case, getting a voter ID if you don’t have a DL is trivial and free, and the only reason for all the objections is voter fraud.
On a related note, all this extended voting / easy absentee voting needs to come to an end as well. It drives up election costs (something few governments can afford) and increases the opportunities for shenanigans.
But Texas is much larger geographically. Some counties are bigger than some of the smaller eastern states.