To TS:
What you have described is the most common lighting setup. In truth, there is no STANDARD or CORRECT way of placing lights. It all depends on what you are shooting. It is just like how you see a large majority of the photographers are using 35mm SLRs instead of rangefinders, medium-format, view cameras etc.
There are a variety of reasons why they appear more commonly:
1. Easy to setup. It is true. It doesnt take much for an amateur photographer to understand much on photography lighting and it is probably the safest method of 2-point lighting (which usually indicates a relatively low budget commercial shoot). You can't go wrong with 2 point lighting. Digital has made it easier, where you don't even need to meter. Check your shots and adjust the power accordingly. If you are referring to school photos (for your school yearbook), the photographer has like so many classes to shoot under a short amount of time. Obviously, the lighting setup will be as versatile as possible (they don't need to make changes to the lighting setup throughout the day), which is of greater importance as compared to say, high fashion photography.
2. They are the cheapest available modifiers. It's true. Many modifiers actually do cost a bomb, including softboxes, lightstrips, grids, barndoors, beauty dishes, ringflashes, etc.
3. Flexibility. You can control the spread of the light on your umbrella by pushing it closer/further to your light. A softbox on the other hand, has a fixed amount in terms of the spread of light. Also, more complicated modifiers require a much longer setting up time. Such setups range from hours all the way to weeks depending on how elaborate the lighting is.
Hope this answers your question.