But systems that lead people to think (correctly or not) that strategy in nomination is no longer helpful to their cause, will likely lead to races having more than three candidates.
You are right that STAR isn't as good with more than three candidates.
What it comes down to, from my perspective, is that to reduce the incentive to strategically exaggerate (*), you need to minimize any reliance on "strength of preference."
STAR does this by doing a pairwise comparison as the last step. A pairwise comparison by its nature doesn't consider strength of preference (as you can see when it is a 2-candidate race in simple FPtP).
Condorcet methods try to do it all with pairwise comparisons. This reduces incentive to exaggerate even further. But since we can't guarantee there will be a Condorcet winner, we'll never get it to zero.
However, my position all along has been that getting it all the way to zero would be nice, but isn't necessary. If you get it close enough to zero, attempts to be strategic will have just as much chance of backfiring as they have of helping. A Condorcet method, including one with a very simple "tie breaking" formula, is good enough. STAR may or may not be good enough. Score is not good enough. Again, this is my opinion, but I it does come from a pretty solid game theoretical foundation.
* technically, incentive to exaggerate isn't the only thing we are trying to reduce. We also want to reduce vote splitting, which creates the incentive to strategically nominate, which in turn causes partisanship and polarization. Finally, we also want to aspire to "one person one vote", so each person has equal voting power. All of these things are accomplished by reducing the consideration of "strength of preference" in the tabulation.