Adding another perspective to the 300GM vs 600PF debate FWIW.
I have owned and shot both. I eventually sold both, and just recently bought the 300GM again. All my experience is only with Nikon bodies though, as I don't own any Sony ones.
For me - it came down to versatility and simplifying my kit. My most used focal lengths are 600mm and 840mm. I own the 600TC, so I have my most used focal lengths covered. but there are often times I just want a lighter kit for hiking, traveling, or outings that aren't strictly photography focused - and I don't want the attention of carrying a big $15K lens around. I knew I would need at least one of the 3lb primes. 300GM, 400 4.5, or 600PF.
The 400 4.5 is the cheapest by far ($2K used), but understandably offers some compromises. I find the naked lens very good, but start noticing degradation with TC's. There is a noticeable difference (to me) between the 400 4.5 + 1.4x and the 600PF, in favor of the 600PF.
The 600PF is the next cheapest ($3.5K used), but it is the least flexible. In my world using the 600PF with a TC is just not going to happen. 840mm f9 or 1200mm f13 are not ideal for me. so I'm essentially left with a one trick pony - great for 600mm, but not useful for anything else.
The 300GM is the most expensive ($5K new/used, $6K with TC's), but has by far the greatest flexibility. As a 300mm f2.8, the IQ and bokeh (to me) are much better than the 400 4.5 and 600PF. Add a 1.4x and you have a 420mm f4 which is more focal length, faster, and still has better IQ than the 400 4.5. Add the 2x and you have a 600mm 5.6 which still is faster and yields better images than the 400 4.5 + 1.4x or 600PF naked, from what I've seen. Up to a point. The one caveat I've found is cropping/super far subjects. the 600PF seems to handle these situations better - but as I try to improve my photography I'm trying to get better at just letting opportunities go, where pictures shouldn't be made. I shouldn't be expecting a 300GM + 2x or 600PF to produce good images on subjects that are 800' away.
After owning all the lenses and trying a bunch of different combos, I find that a 300 f2.8 + 600 f4 is the ideal combo for me. If I went with the 600PF instead, I'd likely also want the 70-200 or 400 4.5. and that just means more lenses, more cost, more weight, and more options. right now I feel that with 1 backpack that holds 2x Z9, a 35-150, 300GM, and 600TC I can cover any situation that I'd want.
I used to also be in the camp of "don't buy the 300GM if it's just going to have a 2x glued to it", but have come around after seeing the excellent work Arbitrage has done. And for me, the trade off in price is worth it just to at least know you can fall back to 300 or 420 if you want. Even if you only use it once a year, it's something you can do - that you can never do with the 600PF. As Doug said above, if I went with the 600PF again - I'd desperately want or need something shorter and faster. The 300GM for me replaces a 70-200, 400 4.5 and 600PF all in one lens.
Ideally Nikon would come out with a sub 5lb 300TC under $7500, and I would run 300TC + 600TC and never want for anything else... but I fear they will try to one up Canon, and instead release a 100-300TC. that would likely be heavier, more expensive, and I don't really value the zoom portion - so it wouldn't be a lens for me. so for now the Sony fills the spot.