I think white noise is fine, unless it eventually bothers you. Some kids like to fall asleep with it and, if it bothers you, then, just before you go to bed, you can always turn it off. I think it falls under the same concept as night light vs. no light. Just a preference. Both my kids are opposite in this area....my son likes it very dark, silent and door shut; my daughter likes a night light and the din of the neighboring room's TV playing, with her door, slightly opened.
If you are talking about "weaning", I'm guessing YOU, personally, do not like it. I know, in my bedroom, I like having my overhead fan on for a variety of reasons, mainly, because of all the knocks that you hear from a furnace or pipes at night - especially when it is windy.
Are your kids even aware that it is on - have you tested that? I would do some experimenting - maybe turning off the older child's noise. They may not even need it although you may think it helps them. Good luck.