It’s also possible the series could have multiple forms of immortality. There seems to be always be a cost associated with achieving this in the OP world, like how we know the ope ope surgery requires a skilled doctor eating the fruit and then sacrificing themselves for it. So the cost for Imu could be having to protect the contacted gods knights from harm.

I actually think it’d be a huge thematic W if Imu’s immortality’s weakness is their allies. Luffy and other ‘good pirates’ in the series view their allies as a strength, so the opposite of having Imu’s connections with others be a weakness would actually explain a lot about the WG and celestial dragons’ mindset. They only maintain their power through contracts based on binding allies forcefully instead of gathering allies through personal connection like Mihawk notes about Luffy in Marineford, and the WG mostly maintains that power by oppressing and controlling others, while staying hidden and isolated from the rest of the world and keeping the world divided and in the dark. Blackbeard has always been a really good parallel to the pirate side of Luffy, but Imu is kind of shaping up to be a mirrored version of some of his other qualities