one argument could be that remote seed logging is low bandwith compared to full remote logging.
I don't think it's a compelling argument (especially in light of all the complexity involved here, etc), but it's an argument.
by the way, it turns out that there is a RFC on how to properly secure logs, RFC5848 that has been through the mill of analysis, both from a crypto point of view and it's limitations (http://www.gerhards.net/download/log_hash_chaining.pdf)