I think candidates might be reluctant to do this, since it could be seen as an admission that the candidate thinks they might not win (although personally I would view a candidate as being arrogant and complacent if they couldn't imagine losing).
You're probably right, though, that candidates should be forced to do this, and maybe they should be able to choose whether or not to disclose their preference in advance to potential voters. If they opt to keep it secret and they win, then their preference never has to be revealed, and if they are eliminated then only their highest remaining preference is revealed.
Admittedly I haven't proved that there aren't times when a candidate may need to tactically reorder their preferences based on the actual distribution of votes, but I can't think of a situation where they wouldn't want to re-assign their votes to the candidate whose values are most similar to theirs / their voters.
You're probably right, though, that candidates should be forced to do this, and maybe they should be able to choose whether or not to disclose their preference in advance to potential voters. If they opt to keep it secret and they win, then their preference never has to be revealed, and if they are eliminated then only their highest remaining preference is revealed.
Admittedly I haven't proved that there aren't times when a candidate may need to tactically reorder their preferences based on the actual distribution of votes, but I can't think of a situation where they wouldn't want to re-assign their votes to the candidate whose values are most similar to theirs / their voters.