How should we control users from doing local archiving?

Export is a different thing. You can deploy the reg keys mentioned here: https://support.microsoft.com/en-sg/help/3058474/how-to-use-outlook-policy-to-control-pst-use-and-creation-in-the-offic

Or disable the Export/Import button altogether (ID 2577): https://docs.microsoft.com/en-us/previous-versions/office/office-2013-resource-kit/cc179143(v=office.15)