Most american cars have 2 to 5...
Engine, Transmission those are essentially mandatory these days on automatic cars. Then you get some that have a Body Controller which handles lights, climate and everything else in one if it's all automated... There are a few odd-ball ones like some Mazdas where it has two separate engine computers, though to regular scanners they both report the same data, a dealership scan tool will pick up extra data from the secondary computer from my understanding. Then you get into luxury cars that would typically always go to a dealership that can have several different computer systems.
They try to keep things as simplistic, but complicated as possible... Like cars with automated headlights here, you have a photosensor that goes to the body controller, and that body controller will turn the headlights on either dim or normal depending on the lighting conditions, then cars with out a body controller (not common anymore) just use a relay system with that photo sensor.
One thing about american cars, depending on the make AND model, the dash lights can and usually do give indications of what could be faulty... Let's say you have a GrandAm, and a wheel bearing speed sensor is malfunctioning, you won't be able to tell which one with out a scanner (yes generic scanner will give the code) but the dash will illuminate three lights, Traction Control, Engine Service, and Vehicle Service, that indicates a hub going bad.
Truth be told, most everything goes to the engine computer or transmission computer here, very little goes to the body computer. The only computer that would need a manufacture specific scanner would mostly be the body computer (or any specialty computer), even then, with the right software package for most scanners here, you can get the codes from that computer as well unless it IS a luxury car, or something like a newer BMW.
Personally... The only time I would ever consider buying a $5000 scanner is if I know I am going to be flashing new code to a computer quiet often, that's one of the only things that a modern DECENT scanner that connects to your computer can't do... But, some companies make and sell specialty scanners that use your laptop for a few hundred that can flash the EEPROM on cars. Far cheaper than the dealership equipment that would normally be required.
Off the top of my head...
Brakes, Transmission, Engine, can almost always be pulled with a decent scanner that connects to your laptop.
HVAC (IF it's computer controlled like it is on mid 90's and newer Lincolns) requires a Dealership scanner (again, $5000 or more), even then, basic trouble shooting steps would apply with an HVAC issue, such as a blend door malfunctioning, don't need a computer to tell me that I am going to have to replace an actuator or stepper motor as it's such a common issue on many different types of cars. But, if you press the right sequence of buttons, you can easily get the display to show an error code that can quickly be deciphered in an FSM.
Body components such as Windows, Lights, Airbags and so on will either be so basic they don't have a REAL computer that performs diagnostics, or if they do have a computer, still basic enough that you don't need a scanner, it's just a luxury to have one for those.
Cars with other special things like backup sensors, automated braking and god knows what else isn't really common enough here yet, though they will be in another 5 to 10 years, I would imagine by that time someone will come up with a cheaper scanner that can interface with those systems for multiple makes and models, or the government *MIGHT* step in again and dictate that they all share a common system for error reporting and diagnostics.
The next thing... If you work on enough cars, and see a common problem with a certain line of cars that comes into your shop, that basic scanner might say give an emissions code, but, 9 out of the last 10 that came in with the exact same symptoms and codes just had a faulty gas cap or filler neck, so you would immediately check that before you poke anything else. In the end it all comes down to experience, troubleshooting, and understanding that you don't have to absolutely have a high end factory scanner to do repairs unless you run into something that's incredibly specialized or unique... And I would hope that someone that has a complicated car or something in the luxury area of automobiles would take it to a dealership where they have the equipment to check things out.