I think that Dumbledore's being tempted by the Hallows shows his human side. There are very few people who would turn down the opportunity for that much power, and he said as soon as he put the ring on, he knew he was unworthy to reunite the Hallows. Through his story, Harry knew what he had to do in the end. Harry is the only one who is able to let the wand and the stone go.
Even Gandalf tells Frodo not to tempt him with the One Ring! Dumbledore's downfall is that he lost his focus, forgot about the cursed Horcrux, and he put the ring on. Luckily he still had the insight to set the wheels in motion for Harry's success, especially since he already knew Harry's connection to the Hallows.