Yes she does, yet he isn't happy with that.
So she isn't putting him first at all, in only being willing to do that.
While he also isn't putting her first at all, in wanting her to do more than that.
Meeting in the middle doesn't put either of them first.
While one of them putting the other first, always does so at the expense of the other not being put first.
It's that simple.
That's why it's nonsense to claim that putting each other first, can be achieved via compromise or acquiescing to the other.
It doesn't have to be a sum-zero game like that. I really don't think it is. I tend to lean toward Dr. Harley's Policy of Joint Agreement, in which putting each other first is a committed state of mind. A husband putting his wife first means his desire is her happiness. A wife putting her husband first means her desire is his happiness. While that could, and probably sometimes does, turn out as one having to acquiesce, the aim is the joy derived from the other person's happiness, which makes each of them happy. Conversely, a person can't find joy in the unhappiness they cause the other. So, it's a win/win proposition, not win/lose.
He's not acquiescing since sex every single day is hardly anything a person actually needs. He's just being gratuitous unless he has some kind of addiction to sex, which it's evident that he doesn't. If they both wanted that, it would be different. Since she doesn't want what is obviously taxing on her and possibly making her feel demeaned, it's not a matter of him having to acquiesce. It's a matter of him NOT wanting her to be unhappy because that should, by virtue of the principle, cause him to be unhappy. The result being his unhappiness in getting what he wants.
You're saying he is unhappy in not getting what he wants due to having to acquiesce to her.
I'm saying forcing her into what she doesn't want to do is what should be the cause of his unhappiness.