Citation Needed (that they actually made everyone equal and it wasn't just a talking point). You may want to read a history book that talks about how Stalin denounced uravnilovka and about the existence of the nomenklatura.
There were a multitude of reasons that USSR collapsed, and reasonable people can argue which were more or less important. I don't think it's reasonable to argue it was due to equality (which wasn't even a thing). Inequality certainly was a thing and one of the reasons, in addition to the Afghan War, Perestroika, Glasnost, the coup attempt, the independence movements of member states. I personally think inequality and structured economic collapse was the biggest culprit.