I don’t feel like that’s the most important thing. If we can farm kidneys for folks with kidney failure, rather than rely on a combination of the kindness of live donors and harvesting organs from corpses, it will be a huge step forward, even if recipients still need immunosuppressants (as they do with human organs).
I do wonder if the immunosuppressants for cross-species organs have to be stronger/nastier than for intra-species organs though.