There are whole countries where virtually everybody has to learn manual, even anxious people.

They just don't have the crutch of automatic gearboxes to fall back on.

Throw her on a hill and she'll see that it's way easier than she expects to find the catch. I'm also pretty high strung, generally speaking, and when I couldn't get a hang of changing gears, the moment would devolve into sheer panic and make everything worse as I snubbed the engine with each attempt. And this was during parking lot practice with someone's old car that they were planning on junking anyways, so no need for that level of stress whatsoever.

But then I was taken to a little incline where I could clearly /feel it/ for the first time and after that, I just "got it".

I have extremely high anxiety and can attest that it took a lot of time and effort to master a stick shift. It's definitely valid that your wife doesn't want to go through that struggle.