Pickaxes are progression tools, not just faster mining equipment. Mining power determines which blocks and ores can be harvested, so some upgrades unlock entirely new resource tiers.
Mining power versus mining speed
Mining power decides what you can break; mining speed decides how quickly you can work. A small speed improvement is useful, but a mining-power breakpoint can matter much more.
Progression gates
Before farming a new pickaxe, check which material or block you are actually trying to access. If the current tool already reaches the needed tier, another upgrade may not be urgent.
Pre-Hardmode to Hardmode
The transition into Hardmode changes the resource ladder significantly. Treat the first Hardmode mining upgrades as part of survival and equipment progression, not a side task.
Mining-run efficiency
Combine a suitable pickaxe with mining potions, mobility and enough inventory space. Tool speed matters less if the run constantly stops because the route or inventory is poorly planned.
When to stop upgrading
Do not replace tools only because a stronger one exists. Upgrade when the new mining power, speed or utility creates a meaningful improvement for your current goals.
Source: Official Terraria Wiki — Pickaxes.