My experience is Lore doesn't have desirability with it, but rather that my players are frustrated because they either have to take Lore dots or, it feels, not be able to come up with their own interesting additions to the setting. Introduce Facts seems to take this ability to contribute, rather than asking me, the GM, for the information, and sequester it away in a single Ability, implicitly stating that this is not a toy anyone else gets to play with unless they go for Lore.

This is why I ask - is it the intention that a player needs to ask me for info rather than contribute their own idea without having to go through me first the way Lore can?

e: basically, it's not about the PCs knowing things, but about the players wanting to be able to introduce setting information on their own initiative.

e2: To better illustrate, a counterexample: Elliot Spencer. Elliot doesn't have huge Lore - he doesn't know a lot about EVERYTHING, he knows a lot about very specific things. He knows how soldiers are going to dress and act, he can identify them by their combat boots or their stance, because it's a very specific stance/boots/whatever. But he's not going to be able to do that for, like, history, or math, or computers, or dogs. He's got a very specific knowledgebase that he can introduce facts on, and that's 'fighting, and people who fight.'