Large knives and axes certainly have their advantages, such as chopping wood and felling trees.
But they also have plenty of limitations (especially in a desert or an area with few trees).
Anyway,here are just few things (off the top of my head) that small knives do better than large knives (and much better than an ax):
Picking thorns and splinters and cactus spines from your body,
trimming broken fingernails or ingrown toenails,
emergency medical procedures (can you imagine doing an emergency tracheostomy with a 12" machete or an ax

),
making notches and triggers for trap construction,
skin small game like snakes, lizards, birds, eels, and squirrels,
carving bones or wood into fishhooks, clothing fasteners, needles and other useful items,
carving eating and drinking utensils,
carving notches for a fireboard,
carving holes to turn a coconut or gourd into a canteen,
making arrows,
making a sling-shot,
making an atlatl for your spears,
making boomarangs and throwing sticks,
making blowguns and darts,
With a multi-tool and a good imagination, the possibilities are endless.