A Singleton is used for shared state between multiple bean instances or bean components. A Stateful session bean is intended to model a conversation with a single client. A shopping cart is the canonical example of a stateful session bean use case. If you went into a grocery store, you wouldn't want many customers using the same shopping cart.
The shared vs. single-client distinction is fundamental to the component semantics. It wouldn't make sense to simply change the stateful session bean model to provide both kinds of behavior.
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