It is Wizarding tradition to either bury or burn a witch or wizard's wand after death.
Most witches and wizards prefer a wand that has “chosen” them to any kind of second-hand wand, precisely because the latter is likely to have learned habits from its previous owner that might not be compatible with the new user’s style of magic. The general practice of burying (or burning) the wand with its owner, once he or she has died, also tends to prevent any individual wand learning from too many masters.
Believers in the Elder Wand, however, hold that because of the way in which it has always passed allegiance between owners – the next master overcoming the first, usually by killing him – the Elder Wand has never been destroyed or buried, but has survived to accumulate wisdom, strength and power far beyond the ordinary.
Tales of Beedle the Bard -- Page 170 -- Collector's Edition
I can't give you an example from canon, except for the bit I quoted previously in another post where Dumbledore does admit to Harry that Dumbledore had intended the Elder Wand to go to Snape.
However, it's never stated whether Snape knew that the wand Dumbledore possessed was in fact the Elder Wand and it would be pure conjecture to assume that Dumbledore had told Snape this fact off-page.
Even if Dumbledore had bequeathed the wand to Snape in his will, perhaps Snape would not have known the significance of this. It takes the entirety of Deathly Hallows for Harry, Ron, and Hermione to deduce the significance of the Snitch, the Deluminator, and Tales of Beedle the Bard. I wouldn't imagine Dumbledore would have made it any easier for Snape, even if he had bequeathed Snape the Elder Wand.
Knowing the Ministry would go over his will with a fine-tooth comb, Dumbledore could not have said outright, "Oh, hey, by the way, this is the Elder Wand. Make sure you keep it in Gringotts." ;) Snape may simply have thought it a sentimental memento were that to have happened. Again, this is conjecture because it's not addressed in canon.
What is addressed in canon is the fact that the Elder Wand seems to have passed from hand to hand via killing and disarming, meaning the Elder Wand has always gone to a live wizard through the generations. Based on the canon available, it would seem that Voldemort was the first wizard to actually remove the Elder Wand from its dead master's tomb (although, technically, Dumbledore was not the master anymore, but Voldemort did not know this).
I've always found it surprising that Harry would actually put the Elder Wand back into Dumbledore's tomb after the Battle of Hogwarts for exactly the reasons you cite. It seems imprudent and risky to me. But that's just my opinion :)
ETA: Thinking further on it, I'm going to err on the side of Dumbledore not telling Snape that Dumbledore was in possession of the Elder Wand. I think that if he had told Snape about the Elder Wand, it would have risked Voldemort finding out where the Elder Wand was, much sooner than he did. This of course presumes that Dumbledore knew of Voldemort's quest to possess the Elder Wand.