Minecraft: When constantly mining cobblestone, how many seconds does a stone pickaxe last for

The first answer in the link you posted tells otherwise, mining with a diamond pickaxe for diamonds works,

1563*4*0.12% = 7.5

and you only need 3 for a pickaxe. The second poster didn't involve the fact that for each block you mine you can see 3-4 new blocks, which just might be diamonds. What he did was calculating the chance if you are mining quarry style and mine all blocks and not only the ones you need to see what all blocks contain.

BTW to improve your diamond mining I would suggest you get yourself a fortune diamond/gold pickaxe and only use it for diamonds.

Also mining for Emeralds is not worth it:

1563*4*0.12%/40 = 0.18756 Emeralds per Diamond pickaxe

Emerald Ore is approximately 1/40 as common as Diamond Ore (40 times more rare then Diamond) (174 Emerald Ore in 2382 chunks, compared to 6637 Diamond Ore). Source

And you need 10 to 11 of them. So you need around 53 pickaxes...

You can indeed get experience orbs by smelting common materials, but you have to use coal or charcoal to do the smelting.

Coal is a limited resource and charcoal requires farming, so this isn't quite a game-breaking XP generation loop.