There is no reason such a state would have to set things up this way.

As an example: you probably know that germany has socialized healthcare. It is, however, not implemented as a single-payer model. Instead there are tons of different insurances competing with each other, while having a highly regulated floor of what they MUST offer.

Is the model perfect? Hell no, it has tons of issues - though overall it's pretty solid. My point is just that social policies and "no internal competition ever" does absolutely not have to go hand in hand. There is a massive middle ground.

See: social democracy as a concept and in its current implementation.