the persons in the corporation would not lose their vote. the corporation is just one additional person, meaning someone could create multiple corporate persons and multiply their vote (at least, in OP's hypothetical scenario)
In reality, the argument is that you can't restrict a corporation's speech because using a corporation to speak is merely a form or method people use to speak.
You could speak via billboards, grass roots organizations, a radio show, lettets, or even a company you own.
The government can't curtail your speech no matter the method.
The people who comprise a group have no extra vote to give: if two friends and I form a group, a new vote allocated to the three of us doesn't magically materialize. By contrast, since there is no quota for speech per person, two friends and I can form a group (eg, an advocacy group) and tomorrow go down to Union Square (or buy airtime, or hand out pamphlets, or stand on a street corner) and engage in whatever legal speech we like, collectively. The claim is that if that group of people happens to be given the structure "corporation", that doesn't automatically allow for infringing on the rights of the people within the corporation to engage in legal speech.
Again, I'm making no statement as to whether I think this approach is wise or good for society or not, but it's astonishing how common it is to see people who completely don't know what they're talking about on this issue and yet are somehow super passionate about it.