Manual or automatic?
I am no tribologist, so this is just anecdote and opinion, but I put synthetic oil in the 5 speed manual transmission of a Toyota once. It started getting noisy soon thereafter, and I had to replace all the bearings in the transmission a couple of years later. I went back to conventional oil.
On my Volvo 245 5 speed manual, I switched to synthetic oil, and a few years later the transmission disintegrated into an unrebuildable pile of metal shavings. I got another tranny from the junk yard and now use only the recommended conventional oil. I have driven another 150k miles on that tranny which had (??) miles on it when I put it in.
If we are talking automatics, some cars built after 2000 call for synthetic transmission fluid. Though it is not ‘permanent’ as the manufacturers suggest, it needs to be replaced very rarely, which is good because it is very expensive. I would not spend the money to put it in an automatic that did not come originally with synthetic fluid.