The system you're proposing would necessarily have to be an opt-out venture. If it were opt-in, you're most likely to not even know about this feature before a stalker has already latched on and gotten your lodestone ID. If the stalker also knew about this feature, they might also start grabbing the IDs of everyone you associate with. Of course, the question then becomes "What functionalities of the lodestone would change if this were to be opt-out?" For one, achievement information for aggregates and surveys would be locked away from third party sites like luckybancho, who use achievement data to track accomplishments in game, as well as population censuses that themselves are pretty popular.

Which, you might answer, is a worthy cost for online protection. I'd typically agree, however it's worth noting that I do not use lodestone much myself so I'm not aware of how the community there works (because as far as I know, there is a community of bloggers there.) I do know people who would abuse being able to hide their lodestone ID to continually harass a community by merely changing their identity every time they'd been ousted, though, so having lodestone IDs defaulted to "hidden" could be a double-edged sword.