A few random thoughts:
Not only can't you erase information, in the MWI I believe you can't
create it either. The constancy of information is another way of
expressing the QM principle of unitarity.
I think it's also tied to time symmetry. Universes with time symmetry
would be unable to create
Wei Dai:
If we consider our observable universe as a computation, it's rather atypical
in that it doesn't seem to make use of the erase operation (or other any
operation that irreversibly erases information). The second law of
thermodynamics is a consequence of this. In order to forget anything
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