The change in literature I've observed during the covid-19 pandemic is certainly prompting this question, but I think the question can be answered broadly in terms of immunology, which does have decade after decade of study, rather than the currently unfolding event.
Here's the claim from various sources, yes they're all about covid, I've yet to read the claim for another disease... but plenty more around covid still, if these aren't enough
These all state you should be vaccinated regardless of previous infection.
To be clear, I'm not asking if it's better to get the vaccine or to get infected, obviously avoiding a potentially fatal, easy to spread disease is the better option - but if you've already been infected and recovered, I've always read that the naturally occurring immunity far exceeds that of immunity gained from a vaccine.
In the case of measles it's well documented the vaccine immunity is sub par to survivors - it was still a huge boon to society, created enough immunity to eliminate the disease in our country (yay vaccines!) until the anti-vax movement led to a critical number of parents deciding not to vaccinate their kids and allowing a recurrence (boo anti-vax).
Again looking at measles, amongst numerous other diseases we vaccinate for, it's well documented that contracting and recovering from the disease provides life long immunity. This article does outline an improperly vaccinated population that could catch it, but also supports the life long immunity claim in recovered patients.
I've only ever read this generally, haven't found good primary sources, and assume it will vary by disease to some extent? But really have no idea, please help out with any evidence.
So is there any evidence that shows a vaccine will provide additional protection against an infection the body already has a natural immunity to?
EDIT: I'm not looking for an expert opinion, strictly hard evidence that shows this. I can find plenty of videos of Fauci saying how important it is. Just haven't seen anything that actually backs it up.