First, all cases are the same in terms of work objects. So, when you create a child case, you still have a case; the difference is the relationship of one case to another.
Now, why use a child case?
A child case allows you to establish a relationship between two very different, but related cases. For example, as a new employee, you are completing the new hire process - and this hiring process is managed by the company. As part of the hiring process, the company wants to conduct a background check - and the background check is contracted to an outside agency.
The company has its own work to do: completing the new hire process with you.
The outside agency has its own work to do: conduct a background check on you.
The new hire process cannot be considered complete until the background check is completed, so you need a way to establish a relationship between these two work objects (cases). So, your new hire process is the main (parent) case, and the background check is a separate, but related (child) case.
The advantage is the built-in relationship between the parent and child case. Imagine a company with 100's of new hires each month; each new hire requiring a background check.
Try designing a case lifecycle that establishes a relationship between each new hire and their background check - without using a parent/child case relationship.
Example: Consider as part of On-boarding process we have a process for assigning laptops to the users. This assigning laptops to the employees will be done by IT Department. If we use the "allotment process" and providing the things with in the same flow, then when the IT Department wants the list of laptops that are newly assigned every month they cannot get information as this is On-boarding case where few people requires laptop and few not.
Now the same scenario, if we go with a separate child case "Allotment" where they provide all the details of allotment every month end they can have the statistics of how many allotments they are doing and they can do predictions using reporting.