In many studios, vocalizing the falsetto range (whistle tone for women) is taken as an article of faith. The rest of us might well ask, "What exactly does it do?"
The falsetto is a partial use of the vocal cords: the cords are dampened, and only the edges are allowed to vibrate. It is a kind of "super light" adjustment. If performed with a loose throat, and without breathiness, it can be a useful way to feel the pitch stretch of the high without the high sub-glottal pressure of the true upper register.
I had a teacher in New York, once, who had his students produce a breathy straight tone falsetto as loudly as possible, before breaking into full voice a fourth lower. The effect for all his students, was an airy vocal production lacking in focus. The voices were robust, but not poised: no one had a good piano, and the forte was dry, but loud. The same exercise, if produced with a loose throat, and no breathiness, can give the student an intimation of how it feels to sing a balanced high note: it all depends on how you do it.
Falsetto, for men, can also give an intimation of the necessary lightness for singing softly: a crescendo from falsetto to piano can nelp you find the mezza-voce, that heady register so necessary in lieder and for certain operatic effects. The challenge is to do it without breathiness, and with a loose throat. Whistle tone, for women, (like falsetto, a partial use of the cords) can also give the feeling of the squeaky lightness required for the highest tones. If done without a feeling for support, and a loose throat, however, it can lead to "cracking" high notes whenever a crescendo is attempted. Without good support, an upper register trained this way will never be really full.
I remember singing Trovatore with quite a famous diva, who had had a vocal collapse, and then been resuscitated by a vocal registrator in California. The voice was beautiful, but whenever she attempted to sing high and loud, her voice cracked. Those squeaks were just not serving her.
Registration by all means: but do it the right way.