When a Tester/Analyst joins a team they'd quickly learn product knowledge by understanding how to test the product and by testing it.
Over time they would learn more and do more analysis, but it wouldn't be old-fashioned "the system shall" analysis, it would be new-fashioned Agile analysis which involves asking "Yes, but how do we know it's finished? What are the test scenarios? Let's flesh out an example or two".
We'd find some Tester/Analysts are naturally more comfortable with the front-of-house work (working with customers) and others are more comfortable with the back-of-house work.
Some of them might even feel comfortable with coding and become tester/analyst/programmers.