"My good friend who lives in Quebec tells me that many couples no longer bother to get married, "
This has been a strong phenomenon since I left Quebec, approaching 20 years ago now. That domestic partnership arrangement you speak of conveys many of the legal obligations and privileges of marriage, although not all.
It's similar to common-law marriage in countries with that tradition, and it is conveyed automatically and without respect to gender. Couples who live together for a certain period of time automatically become "something like married" under the law.
People who live in Quebec say this system offers economic protection to people who may sacrifice career or working opportunities to support their partner for a while. It also offers protection to children and certain limited tax benefits.
Quebecers are quick to point out, however, that people outside the province have some mistaken ideas about the system, that it is not an exact equivalent to common-law marriage, does not convey the same status as marriage, and that legal marriage offers more protections.
When I lived in Quebec, though, my experiences matched your friend's. I saw many more young couples in informal marriages then formal legal marriages.
And I practically never saw women take their male partners' last names, no matter what form of marriage they practiced.