Why won't windows open an application on the same screen where it was requested?

This behaviour isn't something that Windows controls for all applications. Some applications will store and recall their position and size at launch. Those details will often (programme dependent) be stored as x,y coordinates based on the 'main' monitor's top left corner being 0,0 OR potentially from just the corner of the monitor they last resided on.

For example; open notepad.exe. Move it somewhere, resize it. Close it. Open it again. It should open exactly where it last was. These registry keys are where Notepad chooses to store its position. Other applications may also use the registry, or their own configuration store.Registry location for notepad.exe position information


My multi-monitor practices:

Multiple monitor taskbars have improved since Windows XP, but ultimately Windows (and therefore some applications) still lack some of the finer details of multiple monitors. In the Windows XP days I chose to run something like Ultramon to gain some control, but when I moved to Windows 7, I chose instead to centralise my taskbar operations and only use one in the middle (vertically) between two screens. Having now moved primarily to 3 screens at work, I'm back to a single task bar on the main monitor.

To manage newly started windows (since they typically start focused), I use Windows 10's very powerful keyboard shortcuts. Win + (Shift) + Left/Right Arrows. Where not using Shift moves applications between 'restore' and 'Windows Snap' positions, and using it, jumps it between monitors.