It is not a norm. A norm is something in the rubrics such as in the General Instructions of the Roman Missal, established by universal canon law, the bishops’ conference or a province of bishops where they have that authority, by the local ordinary as a particular law where allowed, or as otherwise established by the Church in writing as the way thing are done.
This ‘approach for blessing’ phenomenon is not in the rubrics or the law. It is not established as the way things are done by any office of the Church.
The only *documentation *on this is from the Congregation for Divine Worship and the Discipline of the Sacraments saying it’s not to be done.
What the “majority of churches” do or do not do is actually irrelevant. What they do or don’t do does not establish a norm.
I take it to mean you are asking, “if I went into 100 churches, what would I typically see?” That is actually anyone’s guess. You’d see people doing it along with priests tolerating it, discouraging it, and openly encouraging it. None of which is the norm.