A tow truck is only something you'd call for assistance, not something you fear seeing.
(Parking fines suck, but the municipal ones are usually more reasonable here, even if they don't always get the rules right. It's the parking companies managing large private parking lots, often for free to the lot owner, that are absurd.)
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.
Parking tickets are also considered fees, paid to those managing the parking area (municipality for public roads), as opposed to fines issued by the police or a judge and subject to very specific rules.
