Yes, Jesus does want all of us.
I also believe that as a woman covering my head is more than a simple pious practice, but right now due to change (omission) in the code of canon law 1983 there is (for now) a break in the continuous tradition (and we can say that about a lot of Catholic teachings but that’s another story). Because of that, a woman who believes that she is neither called upon, nor does she desire to (for whatever reason) cover her head at Mass or at prayer is free to do as she chooses.
I do think that, as time goes on, more and more women will choose–and I mean choose freely–to wear a covering, and to attend Mass more frequently, and to engage in many pious practices that have over the last 5 decades or so appeared to lapse or disappear in so many places, such as Family Rosaries, home altars, etc. Many people here already engage in such things. It is a rediscovering and renewed appreciation of the sacred.
I believe something that will draw people is the joy, the humble joy, of women who are choosing and rediscovering the sacred through tradition. Right now because this is something ‘seen’ as so different there are perceptions which are wrong and extremist; on the one hand, the idea that a woman in a headcovering is vain, elitist, proud, and threatening; on the other that a woman not in a headcovering is equally vain, elitist, proud, and threatening. Both positions are wrong.
While the woman who covers I believe will draw others more than those who do not (a situation thus reversing the subtle ‘change’ of the late 1960s and the 1970s where women who just ‘stopped’ wearing coverings seemed to ‘draw in’ women who until then not only wore coverings but did so out of a true respect for God, and whose only reason for stopping was being told both that the practice was not only not respectful but rather ‘a coercion’ and also’ no longer needed or desired), I do not believe that women even today who do not choose headcovering, for whatever reason, are WRONG in their choice; they obey their conscience. I do think though that the more the custom spreads, and the more women receive full, frank, and thorough information of authentic Catholic teaching and practices, that more women WILL cover. . .but again, freely, and thus, with joy, humility, and gratitude.