> Rationing does nothing to increase the supply,
Maybe, maybe not. Depends on how you handle prices (or subsidies) along with the rationing.
>distributes the existing supply to people who don't need it.
A bit, but in the case of housing and food you can safely assume people all need it in about the same amounts. You will be wrong, but close enough. The black market might even by your friend in correcting some of your mistakes.
> Rationing assumes everyone has exactly the same need, which is nonsense and leads to gross inefficiencies.
yes and no. You don't have to assume the same needs. You can figure out rules. Families need more space - which can be used to encourage/discourage having kids depending on your goals. Overall it leads to inefficiencies I agree.
> Rationing inevitably leads to hoarding and a black market.
True or not based on how much trust there is in the ration plan. If people agree with the reasons and means there will be a lot less than if people disagree, or find they can't get even the minimum. WWII rationing in the US mostly worked from what I understand - people were proud to not use their entire ration of sugar, but there was overall enough food (including gardens) so it wasn't hard. That is probably the exception (and even then there was a black market!), but it does make the point.