Yes, this is an unfortunate tie into service providers.
Voicemail is done through service providers, so essentially they're saving voice mails to their network and then you access that network through the voicemail number. We can block the callers, but we can't block voicemails from being saved to your provider and then being replayed on your device.
Rest assured, your kid can't call back the voicemail numbers unless they're safelisted. If you're worried about them listening to these messages, set the passcode to something you both know or something just you, the caregiver, knows.
You may also be able to ask your provider to remove the voicemail system, if they allow that.