When people die, others offer their condolences. Is this helpful at all too? By your logic, you shouldn't accept these condolences as they aren't REALLY PHYSICALLY helpful. But that's not the point is it? The point is that these people reached out and offered their emotional support.
As I've mentioned already, that's a personal thing, and it's being so personal that gives it value. Similarly, offering prayers for somebody specific is a personal way to demonstrate sympathy and provide emotional support. If I post "my thoughts and prayers are with everyone who has lost a loved one today" on Facebook, though, that's not personal. I can guarantee that somebody somewhere has lost a loved one today (literally any day), and could use some sympathy and emotional support, but if I'm not actually going to specify anything about the people I'm sympathizing with, nobody in particular is going to feel supported by that.
That's why it's largely a form of self-gratification. "Maybe somebody affected by the disaster will end up reading my post and maybe they won't notice that it's not at all personally directed to them and they'll feel better" is not genuinely trying to help. It's not putting any thought into how somebody can make a difference for these victims. It's doing the barest minimum possible to feel good about oneself and/or look benevolent in front of their peers, then moving on without actually considering how much good it'll do. That's not caring.
Pretty sure anybody reading it would take at least some solace from it or, at least, nearly as much solace as they would from a "personal" condolences. More so, people who actually know the affected generally *also* offer personalized sympathy to that individual so it's not even an either/or like you're trying to posit. ---