A purely theoretical approach to comparing cello to the human voice is really missing the point.
A cello is close to the expressive quality of the voice. Any cello player will tell you that their bowing arm is their breath. The cello breathes and sings. The frequency range is secondary. The ability of the cello to connect the instrument to the player in an intimate manner, one that allows nuanced expression of the soul of the music is what makes it like the voice. Instruments differ significantly in the way they connect player to the sound.
The classically trained voice has a huge range of frequencies across the possible roles. The cello is one of the few instruments that can match it. (Obviously a piano or other keyboard instrument is much wider.) so there is some basis in frequency range claims, but it isn’t the point. We don’t consider a piano to have a vocal like quality even though it can produce any note a human can.