IMO its as easy for the elites to manipulate the public via media as it is for them to manipulate elected representatives and the latter is easier to address via checks and balances, though nobody seems willing to put them in. Elections are in the public interest so campaigns should be solely funded by the government, not by private backers. Private parties should not be able to run media campaigns on behalf or against individuals. Lobbying would be rendered useless.
Further, certain other countries do not in fact vote directly for their 'most powerful person' -- in Canada, you vote for your representative locally and the party with the most local representatives sends their leader to be Prime Minister, and even there, the Governor General in Right of the Queen has final say just to make sure.
I think as noble as 'I get to decide what matters most' is, it's worthless when issues reach the kind of complexity that requires specialization in your field. As another poster mentioned above, you don't vote on what kind of medicine a child gets, you leave that up to a doctor -- a professional. Now feel free to pick that professional!