Here is an inconvenient fact, a pure falsetto cannot be sustained. The sustained sounds that many students and teachers demonstrate as falsetto are a form of head voice, so called, they are not truly falsetto.. The pure falsetto is hooty, like the bottom notes of a flute. The vocal folds are not adducted; air escapes them. The falsetto, coming from the Italian “falso” is not singable. Again, it cannot  be sustained. What is its value? It enables the tyro to isolate the chest register and begin the work of finding each register in its pure function, the water (here falsetto) and the clay of the vocal mechanism. Isolating the falsetto isolates the pitch making activity of the vocal folds. Sing and sustain a single note in the chest register. Note its qualities. Now execute a note in falsetto, say a above middle c. Just a single note. Return to the same note in chest register and note the change. You may have discovered the virtues of maintaining access to the registers in their pure form.