It's very difficult to study give almost no elite male athletes transition, let alone are studied, and even if they did, they would have the incentive to underperform in any tests.
Lia Thomas went from being a top 600 US male swimmer, to possibly the greatest young female swimmer of all time.
That is someone whose sporting potential was probably to be a good regional amateur, with a new potential of being one of the best of all time, possibly even the best.
That's not an incremental change, but sub-elite to uber-elite.
A US Air Force study on transgender servicewomen found transwomen were on average about 9% faster than other women which would is a massive difference in high level sport
The jump is not so small.
Sometimes a picture can be worth a thousand words though: Laurel Hubbard's, who was a very good, but not elite, weightlifter pre-transition, performance versus other women in her age class.
My personal opinions:
1. We do not start assuming both outcomes are equally likely. The default assumption is that undergoing male puberty will give advantages to transwomen unless demonstrated otherwise.
2. Scientific studies consistently show significant advantage remains
3. There are real-world competition examples of non-elite male athletes becoming elite female athletes after transitioning further illustrating that this advantage remains. These are far more important than any scientific study as these are often severely limited (see next 2 points)
4. While there is no data to show this afaik, with PEDs certain people respond far more strongly than others to the same drugs. It is likely that people will therefore respond differently to performance limiting drugs with them having a much stronger effect on some than others. For elite sport the average may be unimportant, just those who lose the least after transitioning
5. Studies on non-elite athletes are often not even reliable for elite athletes. I'm reminded of a peer-reviewed study that suggested EPO doesn't give any performance advantages leading to some idiot scientist claiming Lance Armstrong lost his TDFs for nothing. EPO obviously worked and we have unequivocal real world data to show this (not to mention the anecdotal evidence from dozens of people who took it while measuring their performance in the most minute detail).
The reasons it's a bad idea don't really relate to the data though, they relate to the spectacle and sporting factors. This is why I say the bad ideas always come from people who don't watch sports.
They are the kind of thing that might be a good idea "in theory", but not in practice as they impact the competition, devalue women's sport and damage the spectacle (and thus funding model) and aren't even remotely workable in team sports or knockout format sports.