(incidentally, my wife is like most people who grew up in Britain...most of them order their steaks/meat well done.)
On the other hand, rare to the point of being cold in the middle, I just do not understand the appeal of it, the texture is not pleasant and neither is the flavor. I think it's just some sort of fetish, hey look at me I'm such a carnivore, or something. Steak tartare, forget it. Ground chuck needs to be at least medium. Rare hamburger is disgusting.
There are quite a few restaurants that would refuse to serve your wife a Filet Mignon well-done. It’s a crime, really, to prepare meat of that cut well done, because a Sirloin would be just as good if it’s going to be burned to a crisp. Overcooking fine cuts of steak is pointless.
The Chef often takes it personally. In her younger days, a Chef once banned my wife from his kitchen for a shift because she brought him an order to cook a Filet Mignon well-done.
In 1957, I was a busboy(today- P/C busser), in Denver Co. The restaurant was billed as “The Finest Steakhouse West of the Mississippi” Served the likes of Jack Webb- Dragnet, Jayne Mansfield(her’s were real- before enhancements). The cfe would not make a steak over medium. If sent back for MW or well, would throw the meat on the floor, step on it, pick it up, spit on it and say “the pigs want burnt meat, I’ll give it to them”. He about burnt it to death.. Lesson learned- Never sent a meal back, anywhere, in the 57 years, since.
correction-—chef
Order the steak the way you want it. If they don't cook it that way, then send it back. After all, you're paying for it.