Restricting the number of votes each voter can cast causes the same problems as FPTP, the so called "spoiler effect". Ideally a voting system tries to get information from each voter about their opinion of each candidate. Why prematurely throw away most of that information?

However, a system similar enough to your example has been used for years by the Quakers, where each voter gives a score of +1, 0, or -1 to each option/candidate. The difference here is that you can give +1 to multiple candidates, and -1 to multiple candidates. Giving your opinion on one candidate in no way limits your ability to give opinion on other candidates.

It's funny we're using this exact voting method to rank the comments in this conversation. Imagine promoting IRV for this: "Everyone just sort all of the comments into your preferred order, and then we'll do these rounds of selection based on that data to pick the top comment. Simple." Sorry, I'm being very unfair -- politics has different tradeoffs -- but the idea amuses me.