I think Ramanujan’s results attained acclaim and notoriety long before rigorous proofs were discovered.
They came to him from God. So apparently divine inspiration can indeed be valuable. Who is to say a Holy Ghost couldn’t divulge secrets of medicine to an anointed prophet.
1 + 2 + 3 + … = -1/12 in the sense that you can factor out the divergence in a well-defined way, and the remainder is -1/12, not 0. Anybody glossing over that divergence is just baiting you, usually for advertising revenue.
But when Ramanujan says 1 + 2 + 3 + … = -1/12 because god told him we accept that as a reasonable explanation.