As it did under Khomeini. Now, there are a lot of positive things to be said for the economies of the Soviet Bloc, usually with huge caveats though - the fall in living standards after the fall of the Stalinist regimes is important to note in this regards (and it's often weakly blamed on "shock therapy", but even states where there was no shock therapy, like the regimes of Tuđman and Milošević, who nationalised everything that looked at them funny and then some, experienced the same fall in living standards). But that there were more babies for the Motherland is not one of them. In fact, generally you expect that as the standard of living and the education level increases, birth rates fall. That the latter did not follow the former in the Soviet Union and similar countries is due to a conservative, narrow-minded, nationalist bureaucracy sitting on the necks of the workers.
Of course socialists advocate for a centrally planned economy, unless by "socialists" you mean people like Ben Bella and his minister for abandoned properties. The thought that, in modern conditions of objectively socialised production, where the production of something as basic as steel or glass requires inputs from around the globe and is required as an input in other production processes (as well as for direct use) throughout the globe, production and distribution can be planned locally is somewhere between quaint and completely outrageous. Not to mention that localism - the stultifying small-town nonsense that some romantic "leftists" peddle - is incompatible with socialism.
And of course central planning can be democratic. As it is impractical to cram several billion people in a room - although this would produce some interesting effects - some form of delegation is needed. But delegation is needed in any case, unless you plan to have groups of about fifty people deciding on resource allocation. Which would either lead to barbarism through the destruction of the productive forces, or to a market (and then barbarism).
As for centrally planned economies, there haven't been any. At most you can have nationally-delimited, partially planned economies embedded in the world market. You can "prove", through practice, that planned economies work about as much as you could "prove" that a global market works in the time of Raymond of Burgundy, the lord of all the Galicias.
Another thing that needs to be considered is - what does it mean to say that a particular way of organising the production of necessities of life "works"? Obviously to socialists the important thing is whether human needs are met. It seems to me, however, that some people (not saying anything about the OP, this is a general observation) really mean that planned economies should successfully compete on the world market. And first of all that's impossible - to the extent that the market exists, planning does not - and second, if a planned economy had money and was efficient in extracting it from the workers, it would not be socialism in any way, shape or form.
Proof that planned economics work?
So why were people in Tajikistan much, much (the gap between New York and Kentucky falls flat) poorer than those in the western cities? Its pretty obvious why. Centralized planning leads to centralization of resources and distribution. Which is a pretty telling reason for why the USSR was 'capitalist' in every sense of the word.
