Which works for standard “screen sharing” apps, where the user is specifically choosing to share their screen or a specific window. However, it breaks for apps that use screen recording for other purposes. For example Bartender or any application that needs to do color matching.ScreenCaptureKit is available since macOS 12.3
The content sharing picker is available since macOS 14.
The system window picker essentially is a way for apps to ask users to pick a window first, then OS presents the content to the app. Since its the OS who is asking the user which window to share, app doesn't need to ask for a screen recording permission as it is granted automatically once the does choose a window.
Apps do not opt to use this new mechanism needs to enumerate the windows themselves, and here lies the problem, users need to first allow screen recording access to the app before app can present to users which window to choose from.
It's very similar to how photos pickers are implemented in iOS and Android.
If allowed by user via a propmt, the OS provides all photo access (or limited photo access in recent iOS/Android versions) to the app, and app draws itself a picker.
However, OS also provides a native photo picker that an app can invoke, the user select the photo, and OS provides those photos to the app, without app ever needing to request permission to read photos. Basically no apps use this, they would rather have access to your all photos, than requesting you to pick a photo and present to them.
Screen capture is a very sensitive permission. Apple wants to discourage usage of previous not so privacy friendly way of sharing your screen. It's not about annoying you, devs can update their app to make their product better but they chose not to.
I get where Apple is coming from here, and I don’t necessarily disagree. However, Apple needs to tread carefully. There is a real chance for dialog box fatigue and, instead of making users more aware of what applications are doing, users become numb to all the dialog boxes and just start hitting “Allow” without any extra thought (or hit deny and then can’t understand why their application stopped working.)