I own quite a number of bicycles that do not have a rear brake and can generate enough stopping power to lift the rear wheel with all my weight thrown back and my stopping distance is about half of those who are only using a rear brake and skidding. I am able to pull off a nearly 1g stop while those using a rear brake can only manage a .5g stop.

This is physics.

This is not to say that a rear brake or a mean to control the speed of the rear wheel is not essential as there are some circumstances where using the rear brake is preferable to using the front... wet and icy roads or loose gravel is a place where you want to be light on the front brake to prevent the front wheel from skidding as if this happens it is usually all over.

Your front brake is the primary and provides nearly all the stopping power, the rear brake should be able to lock up the rear wheel but is best used as a speed modulator... I rarely use my rear brake when I am riding on nice roads in decent weather but do use it when I am riding in inclement weather and in the winter to prevent front wheel skids.

A great deal of how well you stop is technique... this is something I have practised to the point where it has become reflex and my daughters have learned the same in that they use their front brakes to near exclusion unless the road conditions warrant rear braking.