A single, all-round white light on a moving vessel is illegal.
No it isn't.
International Regulations for Preventing Collisions at Sea, Rule 25 (d) (i) says
"A sailing vessel of less than 7 metres (about 22 feet) in length shall . . . . have ready at hand an electric torch . . . showing a white light which shall be exhibited in sufficient time to prevent collision."
An all-round white is quite acceptable.
The IRPCS are applicable world-wide, including Australia and the USA.
Local regulations (especially about safety equipment) are applied within the framework of the IRPCS: the kayak you mention would come under Rule 25 (d) (ii), still requiring an "electric torch" at night.
Conventions may vary.
In the UK the convention is to ignore all rules. They exist only to allocate blame when someone gets hurt!