It raises the costs of paternity testing. Instead of privately, cheaply performing a test, you have to do it publicly and expensively. This de facto stops many men from performing tests, which is significant and not something you can just dismiss. Legal restrictions on consensual activity is not normal and needs a good justification for it. It's the norm to be free to do as you please as long as all parties involved consent.

Maybe you want to figure out if the child is genetically yours before you initiate divorce.