I think that, over time, people would drift towards using only 0 and 10 and none of the middle scores, similar to how, over time a plurality voting system drifts towards only having two political parties (Duverger's Law). 0 And 10 are the "strategic votes" of score voting as 2-major-parties are the "strategic votes" of plurality voting.

A possible counter-argument to this is that score voting doesn't have a reinforcing feedback loop (each election, the minor parties get weaker until they remain at around 1%)

An interesting point. Since you're speaking about strategy and honesty, I would defer to those who have done research, where I can only speak for myself. http://ScoreVoting.net/Honesty.html

I know I would not hesitate to vote my actual opinion and I suspect others would not either. I would be happy to give a score to each candidate, and it would not necessarily be binary. Just as I am happy today to vote for a third-party candidate though that is not a strategic move.

Again speaking just for myself, if nothing else, having the ability to score candidates would reduce my feeling of regret or disappointment with the outcome because it's less polarizing.