I think that vesting direct power in him would likely lead to personality-driven polarization, where people who can't stomach him would be inclined to give their vote to whoever sticks it to him most forcefully. Or other sensationalistic and dramatic storylines, amplified by the media.
Sure but Rush Limbaugh is far more extreme and polarizing than Bush. He could never actually win a primary. But under the proposed system you don't need to.
There's also not the barrier of having to actually be a politician. Someone could make a YouTube video arguing why everyone else is an idiot and they are the only person you should trust with your vote, and the next day have incredible amounts of political power.
For example, if this system were in place right now, how many pro/anti-GamerGate ideologues would overnight go from nothing to having thousands or millions of votes?
If his vote is identical to what they'd vote on their own, what difference does it make?