I say this partly because of the nature of first-past-the-post systems. The rich tend to live in wealthy areas which vote right-wing anyway. Perkins' scheme would thus create even bigger majorities in Tory or Republican seats.
But there's a bigger reason. It's that the rich don't need more votes in order to have disproportionate political influence. They already do, thanks to their control over "business confidence"; our tendency to defer to the rich and successful; the managerialist mindset which serves to justify the parasitism of the wealthy; cognitive biases which reconcile people to even unjust inequalities; and our tendency to be excessively generous to people merely by virtue of the fact they communicate with us.
You might wonder here: if the rich have so much power, why don't they exploit it even more?
Simple. It's because there are two constraints upon the power of the rich, which would exist regardless of how many votes they had.
One is efficiency. You don't have to believe in theories about the inefficiency of existing inequalities to see that, beyond some point, inequality would be harmful for the rich. For example, if workers are so badly paid that they are unhealthy or unmotivated, the rich would suffer as output and profits fall. Similarly, the lack of a welfare state would cause greater volatility and lower labour supply.
The other is simply the threat of a political backlash. Louis XVI and Nicholas II did not benefit for long from high inequality.
A successful parasite needs a healthy host. The smarter parasites know this.
In light of all this, why are so many so outraged by Perkins' comments? It's becauser he's challenging the principle of formal equality, as expressed in "one person, one vote." Formal equality, however, is very different from substantial equality.