The flu isn't a stable thing though, there are multiple strains of what we call "the flu" and its constantly adapting/mutating. Previous infection is no guarantee of protection, just like previous vaccination us no guarantee.

> When is this natural immunity supposed to kick in and stop the elderly and infirm from dying from it?

That's a whole different ball game. You're talking about immunocompromised individuals, their immune system isn't well prepared to respond to natural infection PR vaccination. Vaccines can still help, though they're usually less effective and more likely to cause symptoms similar to the original disease you're vaccinating against.

A vaccine isn't a magic bullet for preventing death. Vaccines still depend on the immune system doing its job effectively.

> Measles mortality fell markedly (>90%) from the 19th century to mid-20th century prior to introduction of measles vaccine or the widespread use of antibiotics for secondary bacterial infections [1][2]

This story is similar for most infections we now vaccinate for, death rates were dropping dramatically years before vaccines were introduced.

[1] https://www.cambridge.org/core/journals/epidemiology-and-inf... [2] https://scholar.google.com/scholar_lookup?title=Measles+mort...