Yes, our Toyota Venza does not have a key, only the push button. You keep a fob on you (or in my case in my purse) and that sends the signal to the engine. You step on the brake, hit the button, and the car starts. There is no key for even the doors.
It's been pointed out that to shut down your car when it's moving you have to hold the button down for three seconds. Many people don't realize this because they don't read the manual. In other words, anything you do has to be with the approval of your car's computer.