Our Blessed Mother has said to pray the entire Rosary, not just one set of Mysteries.

You're absolutely right.  However, most of the people I know, SSPX and resistance can only manage 5 decades per day; and Our Mother did say 1 Hail Mary devoutly prayed was more pleasing than a whole rosary said haphazardly.
Also remember, church tradition before Vat II for the rosary was:
Joyful mysteries         First Sunday of Advent to Feb 2nd  DAILY
Sorrowful Mysteries     Ash Wednesday to Holy Saturday   DAILY
Glorious Mysteries       Easter Sunday to Trinity Sunday     DAILY
All other times alternate  This way we are meditating on the Liturgical Season.
This method can be found in the Raccolta 1857-1940's, Christian Mothers's prayer book, Ideal Missal 1920's or 30's.

You're absolutely right.  However, most of the people I know, SSPX and resistance can only manage 5 decades per day; and Our Mother did say 1 Hail Mary devoutly prayed was more pleasing than a whole rosary said haphazardly.
Also remember, church tradition before Vat II for the rosary was:
Joyful mysteries         First Sunday of Advent to Feb 2nd  DAILY
Sorrowful Mysteries     Ash Wednesday to Holy Saturday   DAILY
Glorious Mysteries       Easter Sunday to Trinity Sunday     DAILY
All other times alternate  This way we are meditating on the Liturgical Season.
This method can be found in the Raccolta 1857-1940's, Christian Mothers's prayer book, Ideal Missal 1920's or 30's.

Another method is to START with the Glorious Mysteries on Sunday (except during Advent when it is the Joyous Mysteries)
Start with the Joyful on Monday and Thursday
Start with the Sorrowful on Tuesdays and Fridays (and M-Sa during Lent)
Start with the Glorious on Wednesdays and Saturdays.
This is a recommended schedule that I read about in a little Rosary book I have.
Some days I just can't manage all 15 but I can get in 10 at least.

That method is the part of the traditional method that I posted that is to be followed after Trinity Sunday to the first Sunday of Advent and also if there is time between Feb 2nd and Ash Wednesday.  It's what I meant when I posted "All other times alternate"
After Vat II they changed the Time After Pentecost to Sundays in Ordinary Time and they wanted to change as much as they could so they had people drop praying the rosary according to the liturgical season and pray according to the alternating method 365 days of the year.

The method you describe is followed by most people now, NO, traditional and resistance.
See how we steadfastly follow the Council.

If it's the only method written in the Raccolta doesn't that tell you something.

I don’t see how that is the Vatican II way to say the Rosary, as the V2 way is to not say the Rosary. 

As I pointed out, members of the Rosary Confraternity are meant to say the full 15 decade Rosary every week, Joyful, Sorrowful and Glorious. 

All in all, the Rosary is not liturgical and these methods are really only suggestions. You could pray all 15 decades a day, or say the Joyful Mysteries on Friday, or whatever. The main point is that we listen to Our Lady of Fatima and pray the Rosary everyday. 

I try to say all 15 decades every day. My wife and I will say the Glorious mysteries tonight for our family Rosary. And it’s all good! Our Lady will happily hear our prayers whether we say the Joyful, Sorrowful Glorious or all the above. 

Our Lady of the Rosary, pray for us!

That method is the part of the traditional method that I posted that is to be followed after Trinity Sunday to the first Sunday of Advent and also if there is time between Feb 2nd and Ash Wednesday.  It's what I meant when I posted "All other times alternate"
After Vat II they changed the Time After Pentecost to Sundays in Ordinary Time and they wanted to change as much as they could so they had people drop praying the rosary according to the liturgical season and pray according to the alternating method 365 days of the year.

The method you describe is followed by most people now, NO, traditional and resistance.
See how we steadfastly follow the Council.

If it's the only method written in the Raccolta doesn't that tell you something.

I'm not arguing with you, I just mean to say that there is more than one way to recite the Rosary since the church does not dictate any particular method.  It is most important to pray it regardless of the method a person prefers.

How can you possibly say the rosary is not liturgical?  It follows the 3 seasons Advent, Lent and Pentecost.
Is the Rosary Confraternity now run by traditionalists?  the SSPX? CMRI? Christ the King? Pius V?
Have you gotten a hold of the Confraternity's old literature from say 70-100 years ago to see how it reads?
Even if it reads the same, what you put forth is merely their minimum requirement.

I merely gave the formula Rome put forth in centuries past, you know the one the saints followed, and yes I'll bet many of them prayed all 15 decades long before Fatima.

This is a traditional site and I only put forth tradition.

P.S.  It really helps with meditating on the season.

I registered with the Confraternity with Dominicans aligned with the SSPX, so yes traditional. 
I’m not trying to argue, but there’s different ways to say the Rosary. There’s the regular method with the Creed, the Pater, three Aves, etc. Then there’s the Dominican form which starts with the Adiutorum and the Gloria Patri. Both are valid. 
Our Lady of Pompeii gave the 54 day Rosary novena back long before V2 which is 3 novenas of alternating Mysterties in petition and 3 in thanksgiving. And that’s valid. 
Or you could recite it in line with the liturgical year. That’s valid. 
These are suggestions. You can pray the Angelus at 1pm or midnight or whenever even though it’s traditionally prayed at noon. And that’s valid. 
What I mean by that it isn’t liturgical is that these are suggestions.  And they all are fine. For liturgy, priests must wear the right vestments, have their chalice, paten etc, celebrate the proper feast. 
Say the Assumption is on a Tuesday. Normally people would be saying Sorrowful on Tuesday. Or you could say Glorious. Both are fine. 

 You can pray the Angelus at 1pm or midnight or whenever even though it’s traditionally prayed at noon. And that’s valid.

I hit the up symbol instead of quote by mistake.
I totally agree you can pray anything, any time.
But the Angelus is TRADITIONALLY prayed 3 times a day:  that is why they ring the church bells at
6 AM, Noon, and 6PM for the Angelus.
My point throughout is merely to show that in centuries past the universal church had the people doing things all the same way.... same Mass, same sacraments, same rosary (depending on which one you were praying) same stations etc.
Ever since Luther, innovations have crept in and Vat II accelerated them.
You can do what ever you want.

I know, I was gobsmacked when I heard JP2 was inventing an addition to the Most Holy Rosary.

Me too. My first thought was (unfortunately) 'it's hard enough to get people to pray the original 3 daily, and now you're tossing in an extra one out of nowhere?'