This would work out the same as your original idea. Richer people pay higher tax rates where there are progressive taxes, so they would end up with more votes.
Your corporation analogy does not hold. It makes sense for stockholders to have voting power proportional to the number of shares they own. They are impacted more by any decisions that are made.
Citizens do not own the country the way investors own a corporation..Each person should count equally. The government provides shared benefits. You don’t, for example, pay school taxes to pay for just your own children. Everyone benefits from having an educated workforce, just as everyone benefits from having clean air and water, and having highways that can be used to go to work and to distribute products.