A couple points can be made about this. First the counterpoint, which is that while your wife may be confident and proud to smooth over those situation that we men would fumble, that same non-threatening nature may have caused her to feel taken advantage of at a car dealership for example. Many women say that male salesperson situations are often disrespectful and borderline creepy.
That also raises the biological question that a lot of people pose. Maybe it's just pure biology that women are comforting on one hand but vulnerable on the other. Maybe it's biology that male pilots (personal example here) react positively to cheerful female controllers but will make fun of a frustrated female controller without hesitation as if she's either an angel or underqualified but nothing in between. Maybe it's biology that white people can confidently travel and express themselves but black people are either praised for conforming to societal norms or shunned for not conforming but nothing in between.
I'm no sociologist so maybe the male/female vs white/not-white comparison isn't valid. Studies on kids have suggested that racial biases are almost purely learned behavior but are gender biases learned or innate? I remember years ago FK mentioned that he tried his best to expose his daughter to all types of toys but over time she gravitated toward girl stuff. He couldn't control for television, or what she learned outside their home. Are these gender roles that seem impossible to control for the same thing as racial roles? Is gender privilege actually comparable to racial privilege? When we talk about "white privilege" do we actually mean "white male privilege" given that, let's be honest, our ancestors pretty much modeled the entire system after themselves and even their own wives were definitely not sitting at the table.
I was trying to make a broader point, which is that we all have some privilege and some burden. My wife recognizes when a less threatening person will likely be better received in a social situation. I wouldn't exactly call myself physically threatening, but when someone is already nervous, they may react much differently to a man than a woman. Similarly, she recognizes when she'll likely get favoritism compared to me, because she's pretty... and I'm a dude.
That's not to say that on the balance my wife has more privilege than other people. I mean, I'm sure she does, because she's pretty. But in any one given circumstance she might be at a disadvantage. A lot of people assume pretty is synonymous with stupid, so if she needs benefit of the doubt when it comes to intellectual aptitude, she doesn't often get it. They come around though because she happens to be very intelligent, but some of that (not all of it) may also be privilege.
I'm at a disadvantage compared to her in a lot of social circumstances. But I'm greatly advantaged compared to other people. Like for example the person I used to see at the pool every weekend who would be wheeled in by two caretakers on a specially designed wheelchair so the he could have a few minutes enjoying the pool before being wheeled back out. That guy was unable to function physically, and I'm not sure how cognitively present he was. He was obviously very much not well. I have nothing like his (presumably) unearned burdens in my life. He's white.
The particular privilege that you were calling out for white people is even more pronounced for women. They have their own gender-specific burdens as well (such as being targets for abusive men), but they do have their advantages. Likewise for being male. Likewise for being white, or black, or hispanic, or asian, etc. Likewise for being able-bodied, or ugly, or beautiful, naturally brilliant, or naturally slow, or artistic, etc. etc.
Too often I feel like white privilege becomes a surrogate for "since you're white, you have it easy" which is exactly why so many people say things like "I haven't gotten my white privilege check this month". Because it does not mean white people have it easy. And all it really means is that racism exists. Skin color is not the biggest unearned privilege or burden you might unfairly possess or face in your life. Not by far.
