That’s a big ask. If I think the vote will probably end up between two candidates I would be fine with winning, I am incentivized to only list the one I prefer. Likewise, if I think the vote will end up going to one of two candidates I would generally not be fine with winning, I am incentivized to list the one I perceive as the lesser evil regardless of my true preferences.
In the end, approval voting comes down to ranked choice voting, but instead of giving ranks you pick a rank threshold where everything above that rank is approved and everything below disapproved. The choice of that threshold is very vulnerable to strategic voting.
I do agree with you that it’s in most cases a better system than plurality though. Even if you strategically lower your threshold to put a lesser-evil type choice as your lowest accepted rank, you do still hand in an approval vote for every candidate above that one. Vice versa with disapproval and strategically raising the threshold.