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Perhaps. But, the eventual winner will not match the rest of the country's views very well, else they would have voted for his party instead of the one they did.

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May I play Devil's Advocate?

Assuming, first, that we could even put together 4 or 5 parties - not likely, but say we did. Those 4 or 5 parties would also be represented in the House and Senate.

If a President were chosen from a ballot of 4 or 5, he would, IMO, be representative of quite a mix of voters. Not totally representing the majority, but that's not done now with 2 parties.

This sounds like the only way our government is ever going to start making decisions based on a wider range of opinions/agendas. Nobody will get anything done without coalitions. Coalitions made up of people who compromised and agreed on what they had in common.

I can see the downside of that, also. Israel's Knesset comes to mind. Not necessarily the best example, either direction.