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If you lose your NemID code card you first cancel it online via your CPR number and your password . Then you order a new one online (identifying yourself via your passport or driving license) and it'll be shipped to the address registered with the CPR card. I have no doubt it's not bulletproof but low-level fraud seems less likely. I'd more concerned about massive irretrievable data loss.
How do you get a new sheet of single use codes when the previous one is lost or destroyed? Why would the process of giving out that new sheet be any better than DVLA issuing a duplicate driving licence? Why can't we follow that process at the DVLA anyway?