Would a recall-styled election work in general elections?

In 2003, California held a special election with a recall of the governor. It was split into two questions, the first being should the incumbent governor be recalled, and the second being if the recall occurs, who should fill the office. This is how Arnold Schwarzenegger became the state's governor. I was pondering the idea of applying that to general elections. The idea is if an incumbent is seeking re-election, the first question would be should he or she be retained in office. The second question would then be who should fill the office if the incumbent is not retained. My line of thinking is that the election is thus primarily a referendum on the incumbent. If the office is being vacated, the first question is not used. I'm not advocating this system, but I would like to gauge how it might be view by the voting public. Thanks in advance.

Public Comments

1. These might be some of the complaints: 1) It would make the ballot longer to have 2 votes to cast. 2) It might favor the incumbent, if his name is always asked first. 3) It might unfairly harm him, if people see his name and vote, but don't read the question "Do you want Joe Smith removed?" 4) If there is no official replacement on the ballot, would you still ask the first question and allow write ins? What if everyone was mad at Joe Smith, but wrote in their own name, making a defeat for him, but no clear winner (Say he lost the first question in a local election 750 out/ 250stay, but no one else was on the ballot officially and the biggest write-in candidate got 75 votes?) I don't see why anyone would want that system, except in recall elections.