There is a good argument against 2. - it means people the CPS do not want to prosecute become above the law. Private prosecutions are a mechanism for prosecuting people the establishment does not want to prosecute.
The CPS can already stop a particular private prosecution - take it over and then drop it.
I agree with 1. The Royal Mail is a de facto monopoly for sending letters (less so for parcels).
If you can't make money by criminalizing the service providers, find new ways to criminalize the act of sending a letter on the demand side.
Brilliant! ;@]
Perhaps:
1. Deregulation and privatization don't work well for some critical services. The BPO should be re-regulated as a government department.
2. Abolish private criminal prosecution, as only the CPS should be allowed to bring criminal indictments.