Beside the before mentioned being bugged to come on a class you don't want, the only other reason I can think of is to hide your craft levels. Other LS members asking you to craft tons of stuff for them and you rather not spend your time breaking 200 crystals or whatever else.

However if this is the case you should probably talk to your LS leadership, and if they are not willing to handle it, or are involved themselves it may be time to move on.

Personally I know leads that use Lodestone profile to check out people that are applying to join. I've used it to quietly check out people in the past who've said "whenever x drops can I have it I'm grinding on it now." Honestly I'm not strongly opposed to it so if they add it I'm still fine, however I enjoy the ease of being able to check out people whom I'm curious about, and check the honesty of people who ask for valuable drops or tell me their new and ask for gear/gil.