Of course that is how you were taught...so was I even before you were born.
The enemies of the church have been trying to tamper with the rosary even in the 1800's.
In the old schedule for praying the rosary people prayed alternating the mysteries for 193 days of the year so it wasn't too hard to get them to extend it to the whole year, especially if they weren't too devout or consistent. It wouldn't take too much; just a few priests introducing it in their parish, someone slipping it in a very traditional prayer book and like sheep everyone followed along; we love new things. We see how effective that strategy worked at Vat II.
For the enemies of the church this got the people from meditating too deeply on the major seasons of the church, Advent, Lent and Easter. Even now look how hard it is to pray the other mysteries out of season.
I only learned of the old schedule when I joined the Archconfraternity of Christian Mothers in the 70's and obtained their manual, Mother Love (now reprinted by Angelous Press). Then about 35 years ago I bought my first copy of the 1858 Raccolta (the first ever printed in English) and the old rosary schedule was confirmed in it.
I can't begin to tell you how many good fruits have come by following the old traditional/original practices of the church. Just don't expect different results by doing the same exercise.
If we want to be Traditional we have to search out the old practices of the church and discard the easier ones that have been introduced. If you pray 15 decades there's nothing wrong with doing one set of mysteries three times. You'll be amazed at how your concentration is strengthened.
Are we traditional or just wannabees?
… “And that old custom of our forefathers ought to be preserved or else restored, according to which Christian families assemble before a figure of Our Lady and alternately recite the Rosary”…. Leo XIII