Freezing your account doesn't prevent you from data breaches, your account still exists in their database, they just say "its frozen" when someone requests it.
That's true, but that's also true of anywhere that uses social security numbers for identity verification (which is an atrocious pattern considering how poorly ssns are anonymized).
Freeze your account and complain to the service that uses it.
Of course, you're not wrong—you have essentially zero leverage.