They failed before computers were widespread, cheap and powerful.
With the amount of data that comes into Amazon, Walmart, Target, and Costco, could you allocate resources correctly in real time?
Yes, sure.
The math is impossible because not all information is available. You don't have future sight and the information you need to derive from is lagging. Its temporally bound to a point in time in the past.
Additionally, the process involves optimizing production from the production raw materials all the way to the end products. This includes knowing about and re-optimizing in the cases where something locally fails sometimes in the absence of people reporting it (non-deterministic).
In non-market systems, shortages cause death, and the only way to avoid shortages is to overproduce by a healthy margin, and even then that doesn't account for those unpredictable events (i.e. for example, like a shipping area catching fire and the nitrogen fertilizer blowing up in Beirut destroying all stored cargo nearby; who could have predicted that).
Anyone saying this is possible isn't a credible source. There is over 100 years of study into this problem by some of the best in their fields, and it remains unsolved.
It's true that non-market economies in the past have faced significant challenges due to the lack of fast feedback mechanisms and the inability to effectively allocate resources. While the advent of powerful computers and the availability of data could potentially improve these systems, it's important to acknowledge the inherent limitations of computers and mathematical models.
As than3 notes, not all information is available, and there will always be unpredictable events that can disrupt even the most carefully planned resource allocation systems. It's also true that solving this problem has remained elusive despite over a century of research by experts in various fields.
That said, the goal isn't necessarily to find a perfect solution, but rather to explore ways in which modern technology can help improve our understanding and management of resource allocation. This could involve developing more sophisticated models, utilizing machine learning algorithms to analyze large datasets, and combining the insights gained from these tools with human expertise and judgment.
In conclusion, while it's unlikely that we will ever be able to achieve "perfect" resource allocation, there's still value in exploring the potential of modern technology and data-driven approaches to improve our economic systems and decision-making processes.