Not all of them, mind. The more precocious ones who indulge in Harry Potter fanfiction will have explored that eventuality. But I can just about hear Hagrid now: "It's an outrage! It's a scandal!" Or I would, if it wasn't about Hagrid.
The evidence is there: Hagrid did seem to take quite a shine to 'young Harry' and his companions. Wouldn't it make for an interesting prequel: Lily Potter, virtually the 'Virgin Mary' of the Gen Y generation, having given birth to the their saviour, Harry…
And who could blame Lily? Hagrid, after all, was half giant. (Bet you can guess which half!)
That's what I realised when I revisited the series Cracker (the British series, not the US series later retitled Fitz for overseas consumption).