Sure, you can always pull out your camera and take a photo of your monitor, but usually what you want is to use a program to grab a screenshot - so that program is what needs to be able to take the screenshot in behalf of the user.
You don't need an app for taking a screenshot. Windows used to include the Snipping Tool I think since Windows 8, and nowadays in Windows 10 it's just functionality baked into the OS: press Shift+Win+S to access it.
You do not need an app for taking a screenshot, but apps can and often do provide additional functionality than the OS - the OS cannot provide by itself every single functionality you may need, its developers may not even think about all cases or consider them important to implement them.
For example while the snipping tool (and printscreen and alt+printscreen, etc) exist, there are tools like Greenshot and Snagit that provide functionality like instant saves to files, better on-screen snipping, an embedded editor for annotations, etc that can be very useful when you want to create many screenshots fast.
Another thing is that some tools may not exactly do what the OS would do (screenshots in this case) but use the mechanism for something similar but different. For example ScreenToGif uses pretty much the same mechanisms for taking screenshots to create short GIF animations from screen captures and then provides a simple timeline editor to for editing the frames, adding annotations, shapes, etc.
The OS simply has nothing like these and it is impossible for it to provide every single functionality that could ever exist.
Note that this applies to other stuff too, not just screenshots.
