Error: "Cannot delete a record type because record type is in use by Package Manager or System Administration profile".
These profiles are not supposed to be accessible as they are used for App Exchange packages. When you go to the Package License Manager profile as an Org Admin, it tells you that you don't have sufficient privileges to change that profile. But the page we really need to get to is the Profile Record Type edit page. It doesn't make the same check on that page, so it's possible to build the URL directly.
For example, build this URL
Instance is the instance the customer is on (SSL, NA1-5, AP, EMEA). You just need to set the ProfileID to the profile ID of the Packaging License Manager (or System Administrator) and the Object to the name of the object (ie Contact, Account or the ID of the object). This then allows you to set the record type to whatever they want the default to be. Then they have the ability deactivate & delete the record type that they could not delete before.
See live example below:
This is a workaround for that scenario.