Competition is inherent to our existence. Not everybody can have a house of gold or even live on the coast. How do you allocate scarce resources? Competition is everywhere.
Nationalizing supplies only hides the true prices and will create a grey market for undervalued goods. Problem is that most goods will be overvalued because, as you write, only capitalists are incentiviced to reduce costs.
No leadership can overcome the misalignment of incentives. The sovjet union could have had better leaders but which resources can they use if managers don't dare to cut costs?
Coops can be more competitive when workers understand that they are not only compensated with money to consume but also influence. At least the unemployed should be willing to participate.
If workers cannot be motivated to support coops, how can socialism be sustained?