Here's my twopenneth worth...
In the beginning, there were solvent extracted/dewaxed Group I mineral base oils. They were cheap, available in huge volumes and almost singlehandedly enabled the mass adoption of the motor car. On the downside, these somewhat aromatic oils oxidised readily (so you needed to change them frequently) and they have limited Viscosity Index (VI). The latter factor was a problem for piston engined aircraft in that to make an oil capable of handling the low temperatures you encounter as you fly higher, you end up with a mineral oil with an unacceptably high volatility (BTW, you can make higher VI solvent extracted Group Is but only at the expense of far lower process yields).
So clever Fritz invents synthetic base oils; both crude PAOs & diesters. They're way more resistant to oxidation because they contain no aromatic structures. They also have inherently higher VI which means you can now make oils capable of handling low temperatures with acceptable volatility. Perfect for keeping the Luftwaffe in the air! There's only one downside & that's that they're very complex to make & very expensive. Typically PAO costs 4 to 5 times as much as mineral oil with esters even more so!
In the years since the war, we've seen various attempts to 'meld' the benefits of both of these type of base oils. Initially the push was to add additives to confer on Group Is, the higher stability & VI that you see with synthetics. There's only one problem with this and that's that all additives tend to push up Noack.
Group IIs, when made in bulk, are if anything cheaper to make than Group Is, are far more stable (less aromatics, no hetro-atoms) but give very little VI improvement over & above Group Is. This means they are brilliant for 15W40 HDDOs where Noack & cold-flow aren't a big deal but where oil longevity is. However use them to make a 5W30 PCMO and you'll hit the age old constraint of high volatility (14.9% might be technically on-grade but IMO it is too high!).
Cue Group III base oils. These are similar to Group IIs but are hit with a far higher hydrocracking severity to get their VI up. This however comes at the expense of lower process yields so they are a bit more costly to produce. You can now make a 5W30 with a decent Noack. You can even make a 0W20 out of Group III but of course Noack goes up accordingly. You can push the severity harder still to get Visom Group III+ but again this comes at a cost.
Now normally you might resort to PAO to make a low Noack 0Wxx oil but Shell figured that using Friedel-Crafts Gas-To-Liquids technology, they could take 'free' stranded gas, convert it primarily to standard fuel products and importantly get a bottoms product that is almost as good as PAO but way cheaper. So they built, at STAGGERINGLY VAST expense, the one-of-its-kind, Pearl GTL plant in Qatar. I'm sure there were lots of reasons why Shell, and Shell alone, went down the path of GTL base oil but I suspect reduced cost over PAO was the main driver.
Personally I like Group II oils used properly and wouldn't much thank you for PAO or GTL on the grounds that neither is worth what it brings to the table...