The USPS includes legal protections against your mail being opened, and a mandate to serve everyone. Whereas private companies can be fully employed for government surveillance (third party doctrine), sell bulk records to commercial surveillance companies (equifax, google, etc), as well as refusing service to whomever they like (ala MC/Visa).

I agree this isn't the overriding concern of those trying to destroy the USPS, but it's surely a nice bonus.