Ideally, socialism isn't just "the government provides for your needs", it goes the other way around too. The point is to come together, pool resources and combine our strenghts. There's no free handouts, you give and you receive.

You shouldn't have to enforce a birth rate cap if the population understand that they need to match society's capacity to expand and build the infrastructure. You'd announce the recommended number and danger number, and people would organically organize to on average make it, knowing their large family could lead to famine.

The main problem here is

If all basic needs were met (food, shelter, and medical)

That part does a lot of heavylifting there. People only play nice all together when society is working for them, people need to respect the society they live in. When scarcity happens, people become selfish, it's survival of the strongest, and everything falls off the rails and naturally goes to capitalism and hoarding resources. The population cannot lose faith in the system.