But this analogy fails at a larger scale - an entire generation can't just save up enough while they work and expect to be provided for in retirement because what they saved up are just claims on future production - their consumption still has to come from the production provided by future generations. Their claims cannot and will not automatically cause the excess production to occur.
Now this is a purely hypothetical problem and we're arguably in a world with the opposite problem (too much productive capacity, too many people trying to save and not enough demand). Though arguably even this problem is due to too many people to save up to prepare for the other scenario, decades before it happens.
How can we model the spoilage of goods and therefore of the loss of value of money that represents a claim to these goods? With inflation. How can we encourage manufacturers to maintain production capacity even in the future? With inflation.