Sure, and plenty of constitutional rights have exceptions with balancing tests. You can't say literally anything under the first amendment, you can't own literally anything that could be used as "arms" under the second, the definition of "due process" is regularly in question when it comes to the fifth amendment and has been a basis of plenty of expansive rulings outside of what you may think is a reasonable part of the amendment.

I was perhaps over-stating when I said "often", but it's not patently absurd that there could be an accepted exception in this case.