Well, you said he excels at the biggest stage. That was only true six years ago, so he did that once. His playing in two big clubs doesn't help him either as he failed to cement a starting place in Madrid and didn't do enough in his loan spell either to be sold and this is where he played in his favorite position most of the time. Bayern went and got on loan another #10 after his return to Madrid. He also got a lot of injuries in the last couple of years and this where his age comes into the picture. You're right about the South American bit, that doesn't usually matter. If you couple that though with his age and him not knowing the league, also for the last 6 years he only played in teams where they expect to dominate every game, do you really think he's worth the gamble?
You might see it as lazy rhetoric but the club tried similar signings like this before and failed and they will definitely be aware of that if someone suggests him as an option for them.
By the ‘biggest stage’, I mean he is comfortable in the shirt at Real and Bayern. He is used to that level, and has played well under the pressure of those shirts.
Ultimately, with any signing, I think you need to sit down and evaluate his motivations. Someone like Gareth Bale is more concerning, as he seems to have little interest in playing football. James joined Real to play, and when he started being left out, he sought a loan, and then if he is now seeking a move so that he can continue his career - it is not concerning, it is commendable.
He was a starter and performed very well for much of his time at both clubs. Bayern liked him, but they are a frugal club, and didn’t want to pay another 42m on top of the 13m they had already paid. Watching the player though, it isn’t that he was rubbish.