“As the closing prayer for the rosary comes out and says,”
You’re making the assumption that the rosary prayer is Divinely inspired.
The rosary was invented by man. Using that as as apologetic for its own words is not logical.
I could make up any outlandish narrative. If someone questioned it, I could reply, “Well, as the closing sentence says...”. I’d be ridiculed.
And my response was to quote the prayer after the Rosary.
I didn't claim that the prayer proved it was divinely inspired.
I was pointing out that the Rosary booklets themselves don't tell you to mumbo-jumble while fondling plastic beads, but to meditate on specific things in the lives of Christ and the Apostles. (The last decade on Fridays one recalls Jesus being nailed to the cross, each of the phrases He said on the Cross, His being pierced with a spear, and His body being handed over to His Mother.)
And, indirectly, by the words of the prayer, to point out that it isn't worship of Mary.
It's not a desperate ex-post-facto backpedaling expedient, either, the prayer's right there in every Missal I've ever seen.