It is my understanding that at least some Dominicans (I have heard “all”, but don’t wish to push a point) do not put stock in St. Dominic having the vision which is ascribed to him receiving the Rosary.
Given that the monks would recite all 150 Psalms, and the great majority of people were not literate (and likely did not have the time each day to recite the Psalms), it seems far more likely.
Given that St Dominic died in 1221 and the first printed version of the Hail Mary appears to be from Girolamo Savanarola’s “Esposizione sopra l’Ave Maria” , it seems strange that it would take that long for it to appear in writing - a bit over 250 years later.
As the most beloved private devotion, it really does not matter whether one believes Mary gave it to Dominic, or it developed out of a desire to emulate the prayer life of monks. What matters is that one prays it intentionally (as in, not spinning through it, but meditatively).
And no, to those who worry and fret if they cannot finish the rosary (distracted, interrupted, fell asleep), that is not wrong, it does not matter; what matters is praying, and praying well and often.