If you want to say "John has a flower", saying "his flower smells good" is fine. But try it with "Someone has a flower. Their flower smells good." Sounds right

If you want to say "John has a flower", saying "his flower smells good" is fine. But try it with "Someone has a flower. Their flower smells good." Sounds right to me. There's no need to replace one with the other everywhere. For example, why would you use "ain't" if you are trying to sound formal and a suitable alternative exists? Just say "No one has time for that." I think it is a strawman argument to equate "there is an alternative word that can be used" (like they or ain't) with "one must use the alternative exclusively" (see how "one" was chosen over "they" in that sentence?)