Presumably you are human, no? The ability to undo a decision at any time significantly reduces the impact of the decision. How much effort do you spend deciding what to eat for lunch? How much effort would you spend if it's what you're going to eat for lunch every day for the next 4 years?
Of course we can. Take the US dominant two-party system, and look at the approval rating for politicians. Look at how many times it crosses the 50% line. Some would only be in office for a few weeks before being replaced, but then who would replace them? What if the previous candidate has a better job already? Does The Party now get to pick someone? How about when approval ratings move back and forth between 48% and 52% over the course of just a few weeks, multiple times?
So that would not happen nearly as often as you might think, and would likely require a fairly major turn of opinion before it would have any effect.
The two party system by the way is very much broken, as is the influence of money in American politics but that's a completely different - and local - affair.
How do you know that about me?
> elections/unelections would cycle too fast to govern
Ok, that may be so, but without trying it we'll never know. You could implement this at the municipal level first, see how it works, iron out the kinks if any are found and then scale it up bit by bit. The whole idea that a politician can say anything and only be held accountable many years later is a pretty big flaw, possibly bigger than the flaw of having multiple election cycles until we find people that do keep their word.