In home wiring, the neutral is connected to ground at the breaker panel.

Then the ground is earth-grounded outside, to stabilize the network's voltage levels. The neutral continues to the distribution network: the current loop is closed by wiring not by conductance of the earth.

Neutral is a circuit conductor that normally completes the circuit back to the source. Neutral is usually connected to ground (earth) at the main electrical panel, street drop, or meter, and also at the final step-down transformer of the supply.

https://en.wikipedia.org/wiki/Ground_and_neutral

The person is indeed safe if there is no closed circuit, e.g. operating with one hand only, and with isolated feet.

This is also why birds can sit on high-voltage lines without harm.

live-line working, also known as hotline maintenance, is the maintenance of electrical equipment, often operating at high voltage, while the equipment is energised. (...) The barehanded approach has a live line worker performing the work in direct electric contact with live parts. Before contact, the worker's body is raised to the same electric potential as the live parts, and then held there by electric connection, while maintaining suitable isolation from the surroundings which are at different potentials, like the ground, other people or trees.

https://en.wikipedia.org/wiki/Live-line_working

In home wiring, the neutral is connected to ground at the breaker panel.

Then the ground is earth-grounded outside, to stabilize the network's voltage levels. The neutral continues to the distribution network: the current loop is closed by wiring not by conductance of the earth.

Neutral is a circuit conductor that normally completes the circuit back to the source. Neutral is usually connected to ground (earth) at the main electrical panel, street drop, or meter, and also at the final step-down transformer of the supply.

https://en.wikipedia.org/wiki/Ground_and_neutral

Then why not dispense with the ground wire, and connect the chassis to neutral? As currents flow through the neutral to supply the device or other equipment on the same line, the potential of the neutral line is raised above the ground neutral, which could pose a hazard if high enough.

A person is indeed safe if there is no closed circuit, e.g. operating with one hand only, and with isolated feet.

This is also why birds can sit on high-voltage lines without harm.

Then there is live-line working, whereby a worker's both hands can be exposed to the same potential, as long as the rest of the body is not grounded, or connected to a line with a different phase.

live-line working, also known as hotline maintenance, is the maintenance of electrical equipment, often operating at high voltage, while the equipment is energised. (...) The barehanded approach has a live line worker performing the work in direct electric contact with live parts. Before contact, the worker's body is raised to the same electric potential as the live parts, and then held there by electric connection, while maintaining suitable isolation from the surroundings which are at different potentials, like the ground, other people or trees.

https://en.wikipedia.org/wiki/Live-line_working