I do not understand why a car should have to pay for parking but a bicycle wouldn’t. Motorcycles have to. Scooters have to. Is it a motor thing? If you have a motor you pay?
Well, if the goal is to discourage motorized traffic, allowing free parking for human-powered vehicles isn’t a bad idea. And, it’s significantly more gentle than, say, charging any motorized vehicle a $5 fee to enter the city limits.
[Edited to add:]Personally, I’d be cool with scooters and motorcycles parking for free too, as they’re still one heck of a lot less impactful than most cars.