Praying the Rosary at Mass is obviously a stopgap measure taken by laity who are heavily marginalized by what is going on around them. There is no possibility that Mass started that way, and for it to become that is a problem to be corrected. It’s always possible to fashion reasons for how one thing expresses another thing, or for how two things fit perfectly together, etc. But the Mass is not the time for the Rosary.
Someone said that the Mass prayers in the Novus Ordo rite are banal, but they are not banal. They mean exactly what they say, and they say a lot. Obscure language is not required to reflect devotion and depth. The Mass was not originally obscure to the people, and for it to become so is a problem that needs to be corrected. It has been, thankfully.
People flee to the chapels because of monkey business at the Novus Ordo. They blame the liturgy, fashioning reasons why the liturgy is inferior: but they are using their intellects wrongly. In a way, those who prayed the Rosary at the Mass prior to the Council were fleeing, although not in the same way. They just used it as a form of participation. It helped them with their sanctification, kept their mind on the things of Our Lord. But it’s an inferior pattern.
Human psychology is complicated. A person may be able to participate very actively while praying the Rosary. But by and large it is not appropriate, and reflects a problem with how the Mass is celebrated. We should never belittle the way people practice their piety, but always help them to a fuller understanding of it.