<<<In regard to installing optional higher wattage lamps, isn't the
purpose of the relay to remove the headlight current from the headlight
switch?>>>

Headlamp amperage draw would be a better analogy.

<<< How would the installation of higher wattage bulbs affect the
headlight switch?>>

Without the relays, you'd for sure melt the headlamp switch ,and the
dimmer switch.

<<Is the stock wiring harness sized for 20-amps of current draw?>>

Sure.
 Each operation of the lamp circuit is fused individully, so if there
was an overload the fuse would fry before the wire.

<< Can you safely install higher amperage fuses in the headlight
circuits without melting down the wiring, fuse block or bulb
connector?>>

Yes.

<< It was my understanding that circuits are fused to protect the
wiring, not to protect the device.>>

Both the wiring, switches, as well as the accessory.