In 2 seconds I could easily pick out a 20-sided dice in a bag with 3 dozen dice and I am not an expert Rogue aided by a magic spell specifically designed for this purpose.The bag has about 3 dozen dice of all types. Many components are very similar, and you don't have 6 seconds to feel around. The 6 seconds includes moving the mage hand to the pouch and moving it back out again as well, so you have only a second or two. AND, you have no tactile feeling, so to be accurate, you'd need to numb your hand before you try so you can't feel the dice. Mage Hands have no sensory ability.
Why do you think the hand does not have tactile feeling? The description strongly implies that it does. If it did not have tactile feeling it could not pick a lock in 6 seconds from 30 feet away ... it could not pick a lock at all. Without tactile feel (and without eyes) how could it even choose the right file from the thieves tools to use in the lock? For that matter how would you take something out of a pack unoticed even if you knew exactly where it was in the container, how would you know when the fingers were around it?
I guess you could say there is no tactile feel and it just does all these things through "magic" of course, but it would have to be one or the other or it could not do any of the things the description says it can do.
Claiming a "magic" hand can not pick something out of a pack because it has no tactical feel is the equivalent of saying someone who uses the levitate spell can't leave the ground because he is not weightless.
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