Sorry, bad idea.
It's not illegal to have no insurance on a parked car -- parked cars don't hit anyone. It's only illegal to take it for a *drive* without insurance.
If you have to let your insurance lapse until you can come up with enough money, there's nothing wrong with just letting your car sit in a parking space until you do.
Depends on where it's parked. If it's in your driveway, a private garage, or otherwise on private property, then you are correct that you don't need for it to be insured, registered, or have a license plate on it.
Depending on the town, parking on a public street may be a different story. In Pennsylvania, for example, it is illegal to park an uninsured vehicle on a public road, so a parking enforcement agent COULD go down the row of cars on the street and have towed any which showed up as uninsured. The most likely reason for not doing that here iis that the two cities with the major problem with uninsured motorists are Democrat strongholds, and the uninsured motorists are mostly Dems.