(That said, I agree plasticity is key to the most powerful systems. A human race with anterograde amnesia would have long ago gone extinct.)
If I'm a human tasked with editing video (which is the field my startup[0] is in) and a completely new video format comes in, I need the long term plasticity to learn how to use it so I can perform my work.
If a sufficiently intelligent version of our AI model is tasked with editing these videos, and a completely new video format comes in, it does not need to learn to handle it. Not if this model is smart enough to iterate a new model that can handle it.
The new skills and knowledge do not need to be encoded in "the self" when you are a bunch of bytes that can build your successor out of more bytes.
Or, in popular culture terms, the last 30 seconds of this Age of Ultron clip[1].
More specifically: it is highly implausible that an AI system could learn to improve itself beyond human capability if it does not have long-term plasticity: how would it be able to reflect upon and extend its discoveries if it's not able to learn new things during its operation?