I know he was old, and therefore having a last will isn't odd, but leaving those specific objects, so strongly connected to the mission that was about to happen now, not in, let's say, 10 years, should've made them think he planned his death.
He simply wouldn't have left those objects if he had died in a couple of years. The Gryffindor's sword should've sealed the deal for them when they figured out it could've destroyed Horcruxes. Dumbledore passed his entire possessions to Hogwarts, but one of the most valuable Hogwarts' objects he left to Harry? As above: he would've never done it if the trio hadn't instantly needed it to destroy the Horcruxes. And he didn't create the testament on the spot when Malfoy attacked him. So, there's no reason why the main characters didn't even mention such possibility.