Then let her work her way up to something bigger.
Unless I am grossly wrong about the meaning of "letting" in the context here this implies to me at least permission. Who knows, though! I have been known to be a foreigner. Worse yet. A foreigner who has seen his wife being talked to by a lot of guys at the range.
My wife is not a big shooter, but she qualified for her CHL with a perfect score just fine even after starting her handgun shooting in the "worst way possible". When we first married 24 years ago, the only gun I owned was a Redhawk .44 mag, which she shot as her first handgun experience.
Odd, that. Or not, maybe because she *likes* what she is doing, rather than for instance my wife who doesn't much *like* shooting anything less than 12 gauge.
I mean, I could "let" my wife start on a .22 and like .... bore her to tears so she never comes to the range with me and then come back about how she simply isn't ready yet to start shooting. Not sure how that helps her shooting, though.
But since "nobody has suggested anything like what you are describing" ...
To do this on the cheap a 22LR is the way to go. I personally think that a good DA revolver is the best place to start. It is simple not ammo picky and will teach her trigger control. The downside is that a good DA 22LR is not cheap. I would look for a used S&W. From here you can transition to a semi-auto for carry or she might find she prefers the simplicity of a revolver.
The next best thing IMHO is a plinker like the new Ruger P22. It is a DA/SA semi-auto gun that will function in a similar manner as most carry semi-autos. This will help her master a DA/SA pull and how to properly manipulate a semi-auto. This will help if the end goal is a semi-auto carry gun IMHO.
As for SA 22LR like a Ruger MKII or 22/22wmr single action I am not a fan of starting people out on these. I love them for later on but learning on a light triggered SA gun can make for a hard transition when you move to DA/SA or DAO carry gun. I love using them to train and develop better accuracy but I do not like them for a first pistol when a carry gun is the end goal. YMMV
After the first pistol course I also recommend a longer training course if you have one available in your area and you can afford it. Creating a good solid foundation for skill development is easier early on vs developing and reinforcing bad habits which become harder and harder to correct down the road.
Again, I am not disagreeing with starting someone on a .22 who wants to start on a .22, but if after a range session, a mag, three shots or whatnot they are eyeing something "more exciting" ... please don't sit there and thump that one "ought to" start on a .22.
"Ought to" or the notion thereof is something I think best avoided, especially when the point of the exercise is to breed a passion.
Seems like you are projecting here...
Beware pop-psychology. It's not really psychology.