If approval voting reduces to bullet voting in heated contests, I don't see that as very bad: to put it crudely, it's just the cost of doing business with that particular voting method, but there's nothing to say the results are compromised as a result. What would be way, way more troubling for the general public is being able to say "but that candidate was the clear favorite, why did the runner-up get the seat?" after the votes are counted. RCV has real, provable problems that will (and have!) create social unrest and a skepticism of the election's results when something like the monotonicity criterion is violated, not to mention the spoiler effect is not completely eliminated under RCV.
Further I believe bounded rationality can be applied here and very many people would still take the approach of filling in more than one bubble even in "strategic" settings, because people aren't perfect rational utility-maximizing agents, and anyway I don't see an acute disadvantage of using approval voting if that's the biggest gripe people seem to have about it.
In short: think of elections in a more 21st-century-Nobel-winner sense, not in a rote 20th-century-econ-professor sense.