But now you'll get an unstable system where candidates get kicked out all the time and are too populist because they don't expect to live long.

So add a low-pass filter. When the moving average of the candidate's support falls below the threshold and a definite other candidate's support is high enough, replace the incumbent with that challenger.

You might even increase the duration of the moving average with time, like the doubling trick in multi-armed bandits. The logic is that a candidate who has shown that he can weather the initial period without getting voted out can be trusted with more long-term decisions, i.e. actions speak louder than words.

Switzerland, people can always overrule politicians decisions there, no need to wait until next election. This means that the opinions of politicians is no longer as important so this issue doesn't even come up. So you place more value on finding the politician best fit for running the country, not the politician with values most aligned to your own.