On a basic level:
"Why change out of first gear?"
"To go faster than 30mph"
For any engine speed, the parts inside the engine are moving. As well as moving, they also have a mass. Given a mass and velocity, they have forces. The faster you spin the engine, the higher the forces get until eventually, something breaks. Added to this is the fact that gasoline engines can only produce torque over a narrow range of speeds, so most car engines will be limited to around 8000rpm because of these factors. You then need the gearbox to provide a tractable thrust curve between 0mph and whatever the cars power and aerodynamics dictate as the maximum speed. If you used one gear for this the car would stall when trying to pull away, just try it for yourself using 5th gear to pull away!
In comparison, something like the Tesla Roadster's electric motor will generate useable torque from 0rpm to 14,000rpm, so it only needs one gear and can produce the same sort of thrust curve as an SI engine with a gearbox.