A voice can be zero shot encoded to a few hundred kb vector. Timbre, prosody, lots of characteristics. That's less information than a fingerprint. And more importantly, that's something you can dial in with a few knobs by simply listening by ear.
It's why your brain can easily hear things in other people's voices. They're not hard signals to reproduce. Some people with flexible vocal ranges can even impersonate others quite easily.
I'm sure most people have gotten, "you sound like X" once or twice. Not unlike the "you look like Y" comments.
Voices really aren't that fingerprint-y.
If we really want to split hairs and argue from biology, who "owns" the voice of a set of identical twins?
But still there are some voices that are just highly associated with just one person in everyone's minds, like David Attenborough. For example, if I heard Attenborough speaking my local train announcements, but it would be an impersonator, I think I would feel like the company is taking advantage of Attenborough's voice. I.e. they would be using the fact that everyone knows this voice to their advantage, without actually paying Attenborough.
While voices aren't technically that unique, when linked to certain situations or when heard by enough people, they become unique in that context. I'm sure no one cares about Attenborough's voice 100 years from now.
Or hm, maybe AI voice tools will keep his voice alive forever in Planet Earth spinoffs, just like Sinatra has been resurrected for mashups.