The system that elects billionaires is the same as the system that elects our government.

Perhaps billionaires will spend their money more efficiently.

But they'll spend less of it on the public good.

The government may be less efficient (also, citation needed there, as I don't buy that at face value), but even if it is it has access to WAY more funds.

Sure, we have some nice billionaires like Zuckerberg and Gates who give their money away, but if you required all the billionaires to give up some money, you'd have a much larger pool to work with. So efficiency isn't the only part of this argument. There is also volume.

If you force rich people to give away a large enough percentage of their money, perhaps you will remove any incentive for the non-philanthropic ones to keep earning more money. If they weren't inclined to give it away in the first place, they probably won't be inclined to make more, knowing they'll be required to give it away.

And therefore the people who end up making the most money are the people who are the most philanthropic and that is worse than the current system how?

Because those people are already giving most of their money away to causes that benefit the world. The "other" rich people are still, on average, creating wealth though, via the companies they start and run. If you disincentivize them from doing those things, you eliminate that wealth, leaving everyone worse off on average.

Hope you're ok with whatever that billionaire's vision is.