I don't know of a country that requires all bicycle parking in any non-private location to be paid, nor a country that requires payment for roadside parking on country roads outside cities. Heck, even within cities, only the very dense ones seem to require paid parking on smaller roads.

Public space does not imply free of any use, but rather that it is freely used by all. The purpose of paid roadside parking is to reduce demand on what quickly becomes a limited resource in dense cities.