I don't really see how you can interpret "a team clearly on the way down" as "a bunch of rag-bags and ne'er do wells." City had won the title in 2014 with a team which had totalled 86 points and scored 102 league goals. This had fallen to 79 points and 83 league goals the next season and in Pellegrini's final season City finished fourth wit 71 goals and only 66 points, only fourth on goal difference. That id a team in decline, "a team on the way down".
The players you name all deserve a place in, not only our hall of fame, but that of English football. But if we look at the squad Pep inherited we can see clearly that Pellegrini's time in charge had been marking time. De Bruyne and Sterling had been bought but it seems that Pep played a role in this. Ya Ya was34 when Pep arrived, Fernandinho was32, Kompany and Merlin both 31 and Sergio a youthful 28 when Pep took over at the Etihad. In addition 6 other regular first teamers were over 30. The entire back four were over 30: Di Michaelis had just left aged 35 and Sagna, Clichy, Zaba and Kolarov wereall in their thirties as was Vinnie who, plagued by muscle injuries, had played only 10 PL games that season. Otamendi was the youngest defender and he was "only" 29! Our full backs were unable to attack down the wings and then get back and our real speed merchant, Jesus Navas, was as old as Clichy! Pep's first task was to begin the rebuilding and reduce the age of the squad; if we assume our best eleven was Hart, Zaba, Otamendi, Kompany, Kolarov, Fernandinho, Ya Ya, Silva, de Bruyne, Sterling, Aguero, how many were over 30 and in the twighlight of their careers? Half that team - which accounts for the "half a team later" comment I made. The 2015-6 team needed an immediate infusion of younger legs and a complete rebuild in the course of the next few years. The younger legs came in the windows of 2016-17 and the complete rebuild of that 2015-6 will come in the next two years as the survivors of that team have to surrender to Father Time.