Why does the bike-rider system need a lean angle when a motorcycle follows a steady road-speed curve?

Answer: The road pushes the tires inward while gravity pulls down, and the lean lines those forces up

The road pushes the tires inward while gravity pulls down, and the lean lines those forces up ✓ — Correct. In a steady curve, the road must push the tires inward while gravity pulls down, and the bike-rider system needs those effects to line up through a lean angle. Lean is not styling; it is the force balance that makes the curved path stable.

An upright bike-rider system can stay balanced because the tires grip the road well enough — Staying upright is the tempting intuition, but an upright bike-rider system cannot balance the sideways force needed for a steady road-speed curve. The turn requires inward tire force and downward gravity to work through a lean angle. Lean is the practical way a two-wheeler makes that balance possible.

Pulling on the handlebar alone can balance the cornering forces without any lean — The handlebar helps set lean and steering angle, but pull alone cannot balance the cornering forces. If the bike stayed upright while the path curved sharply, the required inward push would create a tipping problem. The stable state depends on lean, road support, gravity, and tire force together.