Mobility affects almost every part of Terraria. Movement upgrades can improve survival, exploration speed and boss consistency at the same time.
Horizontal movement creates reaction time
Faster or more reliable horizontal movement gives you more space to respond to attacks and cross dangerous terrain.
Vertical movement opens exploration options
Better jumping and vertical control can make caves, arenas and surface travel significantly easier.
Build arenas around your current mobility
A useful arena matches the movement tools you actually have instead of assuming later-game equipment.
Fix movement before adding more damage
If the main reason you lose is poor positioning, damage upgrades may not solve the encounter.