Cars that unlock without pressing anything or by pressing a button on the door look for the key that is bound to them. It is secure in that only a key programmed to the car can tell the car it is ok to unlock. They keys are authenticated with a rolling code that is synced between a car and key when the key is programmed to the car. Thieves clone the key's signal and then the car has no idea that the fake key is not the real key.
You can't hotwire a modern car. On a modern pushbutton ignition car the starting function is allowed through a security module that makes sure the key is there before starting. Pushing the button only asks permission to start the car and then the module is the one that tells the car to start.
Lock-picking a modern car can be done, but it is far easier to use a wedge and inflatable air bag to pry the door open enough to use a hooked tool to open the door from the inside. Nobody picks automotive locks anymore, a lot of the door locks can be ripped out and bypassed anyways. You can of course just break the glass, but it may sound an alarm. The F150 has a massive theft issue Ford won't bother to address, the alarm can be disabled from outside the car using no tools whatsoever.
Once a thief has access to the inside of the car, they can program a new fake key using specialized software which is usually dealer level software but it can be done using 3rd party software. You can't just ban all non-dealers from having the capability to reprogram keys, that is user-repair hostile and would mean you have to pay whatever the dealer wants to replace a lost or damaged key. Not to mention that thieves will still find a way to access dealer tools and keep on stealing anyways.
A lockout period wouldn't accomplish anything, the original key still gets cloned and can be used to drive the car away. Once the stolen car is taken, the thieves have all the time they want to reprogram a key.
Enhancing security measures by using a more secure key authentication method will only go so far as to preventing theft and will add considerable costs to cars and key replacement. Thieves will catch up to any means of securing cars. A better solution is to improve economic prospects and enforce the current laws effectively to remove incentive to steal cars.