Microsoft explains the oldest annoyance in Windows: why Task Manager freezes exactly when you need it
Something goes haywire, the fan spins up, and you reach for Task Manager. It opens a blank grey rectangle and sits there. Raymond Chen, who has been writing Microsoft's The Old New Thing for twenty-odd years, took on the question people have been shouting at their screens for just as long: why not simply run the taskbar and Task Manager at high priority so this cannot happen?
Because priority decides who gets the processor next, not who gets to skip the queue entirely. Chen's analogy: a priority checkout pass gets you to the front of the line, but if the person at the register has a trolley full of shopping, you wait anyway. His blunter version is that "unless you have been very careful to avoid it, you will eventually run into a shared resource that you will have to wait for." Task Manager has to draw a window, and drawing means competing with every other interface thread on a machine that has already run out of room.
Windows does already give the program you are looking at preferential treatment. So the useful move is getting Task Manager into focus in the first place: Ctrl+Alt+Delete reaches the secure screen, which is a separate path and often responds when the desktop will not. Better still, turn on the End task option under Settings, System, Advanced. It puts End task straight into the right-click menu on the taskbar, so you can kill a stuck app without opening anything.
That covers the occasional runaway. A PC that drags all the time is a different problem, usually too much launching at startup or an update that never finished, and Tendvane's health score is built to point at which of those it is.