Isn't this still assuming we can even determine what is true or false?
Newtonian physics is false, but it works well enough we teach it in college. But our best models of physics are currently in disagreement, so can we even say they are true? Given the replication crisis, especially in social sciences, how many of peer reviewed findings can be called true? Even experimental results can be false (consider studies that found FTL neutrinos, which were rejected as an error in the experiment, and which was eventually confirmed but it took quite a lot of work and in a softer field than physics with a claim less absurd than FTL, would have likely long been accepted as a true finding).
Even in math, basic statements aren't really true or false, but more a question of "given these axioms, can we prove or disprove it" noting that we have different systems with different axioms. If we are talking basic sets, most people are using naive set theory which is inherently contradictory, which means that notions like true or false probably can't be considered well defined.
True and False in general communication means based on best available evidence and expertise statement contains no obvious contradictions or falsehoods based on an optimistic parsing of meaning language and intent. Notably this leaves out misleading or missing data because those concerns are separate from truth and falsehood.
E.g. if I say the earth is round we optimistically parse round to include oblate spheroid and rate it true.
If I say that the earth is flat we rate it as false because there is no reasonable interpretation possible other than confusion or malice.
Newtonian physics doesn't just work well enough for education. It provides an incredibly accurate and precise model of the world except at extremes. The majority of engineering does not necessitate using theories of relativity. Both theories are incomplete models approximating reality and are very far from being false.