Why didn't Dumbledore simply put the Philosopher's Stone into a mokeskin pouch?

In HP and the Deathly Hallow Harry receives a mokeskin pouch for his 17th birthday. Hagrid vouchsafed that anything inside was inaccessible to all but the owner.

‘Here, Harry – couldn’ think what ter get yeh, but then I remembered this.’ He pulled out a small, slightly furry drawstring pouch with a long string, evidently intended to be worn around the neck. ‘Mokeskin. Hide anythin’ in there an’ no one but the owner can get it out. They’re rare, them.’ ‘Hagrid, thanks!’

Why then did Dumbledore not simply hide the Philosopher's Stone in a mokeskin pouch?