It (unfortunately) makes sense, as I recall Rowling saying in an interview that it would be far worse to lose Hagrid than another character (I don't remember which one it was).

If Dumbledore has a Horcrux (Fawkes), then Hagrid is the secret-keeper as Dumbledore *literally* trusts Hagrid with his life...remember DD told McGonagall this at Privet Drive in book 1.

So losing Hagrid would also mean losing Dumbledore for good. That is why it would be far worse to lose Hagrid.