Being 'well-adjusted' isn't a privilege. The language of privilege is really misplaced here. Privilege is a right or set of rights that has been granted to some people and not others (by an institution, a nation, a powerful person or class, or in some cases by society).
It suggests social injustice, and puts the alleged privilege-bearer on the defensive, feeling the need to give way in relation to their own interests in order to compensate for the alleged moral wrong of their advantaged position.
None of this is remotely fair or accurate in relation to being 'well-adjusted'. You could call the good adjustment 'lucky' if you want, but even that is unfair, since 'well adjusted' isn't just about the absence of trauma, it is also about whatever intrinsic personal attributes helped to shape that person's response to the life events they have been through. These may include a whole range of good, bad and neutral characteristics, including, say, a willingness to keep on plugging away in the face of adversity, or just a rather unquestioning, low ambition approach to life.
Are each of these characteristics to be regarded as privilege? In that case every single one of us has a cluster of 'privileges' - personal characteristics which may help us in certain situations. It's completely absurd. None of us has free will, we are all shaped by a huge multitude of internal and external factors, many of which will help us in specific contexts and hinder us in others.
I'm so sick of this endless, endless desire on the part of so many people to find ways of creating a special victim identity for themselves, and in the process creating a myriad of 'privileged' people whose job it is to 'make allowances' and find ways to signal their allyship.