"They can only approve of one" is FPTP, the existing system. Everybody knows that sucks. The whole point of approval or score voting is to avoid that.

Right now if you favor candidate C but they have 5% of the vote and candidate A and B each have 45%, your preferred candidate has no chance and your vote can only change something in determining whether the winner is A or B, so you avoid voting for your preferred candidate.

With approval voting you vote for them and one of the major parties. Then people notice that third party candidates are immediately getting 30-40% of the vote because the people afraid of wasting their vote no longer have to refrain from voting for their preferred candidate. In some districts they even win. Which dissolves the two party system because people have to take third party candidate seriously and starting a new party has a real chance at succeeding rather than being an exercise in futility.