I think the value of a state machine is treating all of the associated states in a single conceptual model or level. You can definitely do everything directly in a bunch of if statements and tracking state in separate variables, but that opens yourself to more potential bugs, higher maintenance cost, less big picture understanding, and even larger performance costs (separate codes means the compiler can't optimize as well; means hardware caches aren't as effective; there's more overhead to run separated functions; etc, etc).
Here's hopefully a more apt example: imagine wanting to have a multiple document interface (MDI) that shows a bunch of 'window' like views. Some examples of the idea are react-grid-layout, golden-layout, react-mosaic. Each window can be minimized, maximized, moved, flashed, and closed ... all with flashy animations. You could create a whole bunch of components that allow you to capture all the different states and toggle them in different components, and effectively have the MDI business logic sprinkled all through out YOUR code, not just the 'library' code. Alternatively, you could use a state machine that captures all the states in a single spot and manages that all efficiently and safely, you just call an api to trigger state changes throughout your code.
As some other comments have mentioned, this is a fundamental part of computer science. You can get by without knowing it cause you can write a bunch of ifs and state logic all over the place. If you only know how to use a hammer, ya you could still hammer a screw in. Understanding how different data structures of different patterns fit together provides you new tools to do things in different ways when appropriate. Learn how to manage complexity, not fear it, cause there's nothing dangerous about state machines. In fact, I'd argue that anyone that thinks state machines make things more complex just isn't looking at a large enough scale because state machines should make things less complex by wrapping all the complexity inside them (when used appropriately).