Can the default contact store for Mountain Lion be iCloud? I'm struggling to manage duplicate contacts and would like to entirely and permanently disable the "On My Mac" category for contacts.

I never, ever want a contact to be added to a Mac and not be stored in iCloud.

Have I missed a setup step since I'm ending up missing contacts on my iOS devices when my Mac decides to store things locally instead of globally.
You missed a step when setting up iCloud.

On each Mac, you can set the default account to be iCloud in the general preferences.



Now, you'll need a short clean up to migrate all your incorrectly filed contacts. 


Select Accounts and temporarily disable each iCloud / Exchange / online account.
Then export all the "On My Mac" contacts to a vCard file and delete them (you have a backup of your Mac and if paranoid, a full export of all contacts before you delete things, no?)
Once things are clean, enable the default account, check that it's set like above, and drag the contacts onto the "All bike@whatever" 





Import all the contacts, even if there are duplicates as you can then have Contacts look for duplicates and merge / update existing contacts as needed.
Once you've deleted all contacts from On My Mac and deselected it as the default, Contacts should hide that group from view and simplify your contacts going forward.
At this point, optionally enable other cloud contact sources and re-verify the default account.