As per
this page,if we strictly follow MC rules,he's actually making it harder for himself.
Not counting the material of the tool,the blocks' own hardness value is multiplied by 1.5 if it can be harvested,which requires the correct tool of the minimum resource type.
Stone is above the minimum,but he's using an axe,so he is instead getting a base FIVE TIMES multiplier on what we can assume is a cobblestone floor.
So what would've taken 0.75 seconds to harvest using a stone pickaxe(1.5 for wooden)is now 10 seconds to destroy using a stone axe(which is the default,bare handed).
But also yes,an axe does have a higher damage multiplier then a pick(if crits were done differently and armour penetration was included,a pick would do better for that)so it is better for self defence.
So the real play here is to first make a pickaxe then make an axe.
Alas,what he's going to make next is baby slimes...