No it absolutely is the way to win in the fewest moves. When you have more than 2 equally possible words then the next word should be a choice that reduces the search space rather than going for a guess.
It's the way to win in the fewest words on average.
If you want to maximize your number of three-guess-wins even if your 6-guess-failure rate is higher, it is obviously can't be a correct strategy to use your third guess on a word that you know can't be correct.
It's a gamble. 20% 3-guess win/80% 4-guess to FAIL or 100% 4-guess win.
Maximizing information from each guess until the answer is down to two candidates minimizes the number of guesses needed to win.
Sure, my point is that the metric "minimize mean number of guesses to win" isn't axiomatically the objective function: the 6 threshold already suggests that many people would rather have a "guaranteed 6 and average 5" rather than "average 4 but fail 5% percent of the time".
If someone considers a 4 to be a soft-failure then they will prefer (3,6,6) to (4,4,4) even though the latter is a lower mean number of guesses: it's a higher count of 4+ 'failures'. The strategy that considers (3,6,6) a better result than (4,4,4) wouldn't guess "dream" in the above example.
This, again, depends what your goal is, or what you consider "winning". If you're only focused on avoiding losing, then yes this is the right move. If you're trying for a low score, it's not as clear, and hard mode may actually be "easier" in many ways.