What is the point of them??? At the risk of stating the obvious...
The purpose is Traffic Control
The signs are designed to warn drivers about pedestrian activity and cross traffic, and cue them as to who should be stopping for whom.
How does that work without the government jackboot on the driver's throat? This may be hard to understand for fans of Mad Max, but...
Some people view the system of personal vehicles and roads as a wonderful gift. They want the system to work, and they think cooperatively. So they want traffic controls to help them drive more safely and to resolve operation sequence at crossings. They understand the value to helping everyone drive more safely without unfortunate incidents. They obey the traffic controls voluntarily.
...and..... if you choose to not cooperate, you'll be hitting them a lot, and it will be your fault.
Now, how does this work in the law?
First, hitting another car with your car may be illegal on private property depending on jurisdiction. But it's definitely a civil tort on private property. That means they get to sue you for their damage, even though you never see the legal process because it is done behind the curtains by the insurance companies.
In that legal action, they will look at the "facts on the ground", including any traffic controls regardless of whether a cop had jurisdiction to write a ticket. They only care about who is careless, and the existence of that sign is a very strong factor.
In most states, property owners (think: large retail properties, like malls) are allowed to invite the police to come on their property and enforce traffic law. Most malls do. In which case a traffic stop in that "agreement" mall is the same as a traffic stop on the highway. You don't get a say, the property owner does.
And, with handicap spots in particular, the legislation in your state certainly provides for enforceability of handicap spots on or off private property. Otherwise, the law wouldn't be much good, would it?